Point Group C30h

ε=exp(2πi/30)
C_30h	E	C₃₀	C₁₅	C₁₀	(C₁₅)²	C₆	C₅	(C₃₀)⁷	(C₁₅)⁴	(C₁₀)³	C₃	(C₃₀)¹¹	(C₅)²	(C₃₀)¹³	(C₁₅)⁷	C₂	(C₁₅)⁸	(C₃₀)¹⁷	(C₅)³	(C₃₀)¹⁹	(C₃)²	(C₁₀)⁷	(C₁₅)¹¹	(C₃₀)²³	(C₅)⁴	(C₆)⁵	(C₁₅)¹³	(C₁₀)⁹	(C₁₅)¹⁴	(C₃₀)²⁹	i	(S₁₅)²³	(S₃₀)¹⁷	(S₅)³	(S₃₀)¹⁹	(S₃)⁵	(S₁₀)⁷	(S₁₅)¹¹	(S₃₀)²³	(S₅)⁹	(S₆)⁵	(S₁₅)¹³	(S₁₀)⁹	(S₁₅)²⁹	(S₃₀)²⁹	σ_h	S₃₀	S₁₅	S₁₀	(S₁₅)¹⁷	S₆	S₅	(S₃₀)⁷	(S₁₅)¹⁹	(S₁₀)³	S₃	(S₃₀)¹¹	(S₅)⁷	(S₃₀)¹³	(S₁₅)⁷
A_g	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
B_g	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1
E_1g*	1 1	ε^* ε^*	ε^2* ε^2*	ε^3* ε^3*	ε^4* ε^4*	ε^5* ε^5*	ε^6* ε^6*	ε^7* ε^7*	-ε^7* -ε^7*	-ε^6* -ε^6*	-ε^5* -ε^5*	-ε^4* -ε^4*	-ε^3* -ε^3*	-ε^2* -ε^2*	-ε^* -ε^*	-1 -1	-ε^* -ε^*	-ε^2* -ε^2*	-ε^3* -ε^3*	-ε^4* -ε^4*	-ε^5* -ε^5*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^7* ε^7*	ε^6* ε^6*	ε^5* ε^5*	ε^4* ε^4*	ε^3* ε^3*	ε^2* ε^2*	ε^* ε^*	1 1	ε^* ε^*	ε^2* ε^2*	ε^3* ε^3*	ε^4* ε^4*	ε^5* ε^5*	ε^6* ε^6*	ε^7* ε^7*	-ε^7* -ε^7*	-ε^6* -ε^6*	-ε^5* -ε^5*	-ε^4* -ε^4*	-ε^3* -ε^3*	-ε^2* -ε^2*	-ε^* -ε^*	-1 -1	-ε^* -ε^*	-ε^2* -ε^2*	-ε^3* -ε^3*	-ε^4* -ε^4*	-ε^5* -ε^5*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^7* ε^7*	ε^6* ε^6*	ε^5* ε^5*	ε^4* ε^4*	ε^3* ε^3*	ε^2* ε^2*	ε^* ε^*
E_2g*	1 1	ε^2* ε^2*	ε^4* ε^4*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^5* -ε^5*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^5* -ε^5*	-ε^7* -ε^7*	ε^6* ε^6*	ε^4* ε^4*	ε^2* ε^2*	1 1	ε^2* ε^2*	ε^4* ε^4*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^5* -ε^5*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^5* -ε^5*	-ε^7* -ε^7*	ε^6* ε^6*	ε^4* ε^4*	ε^2* ε^2*	1 1	ε^2* ε^2*	ε^4* ε^4*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^5* -ε^5*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^5* -ε^5*	-ε^7* -ε^7*	ε^6* ε^6*	ε^4* ε^4*	ε^2* ε^2*	1 1	ε^2* ε^2*	ε^4* ε^4*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^5* -ε^5*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^5* -ε^5*	-ε^7* -ε^7*	ε^6* ε^6*	ε^4* ε^4*	ε^2* ε^2*
E_3g*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*
E_4g*	1 1	ε^4* ε^4*	-ε^7* -ε^7*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^5* -ε^5*	ε^6* ε^6*	ε^2* ε^2*	ε^2* ε^2*	ε^6* ε^6*	-ε^5* -ε^5*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^7* -ε^7*	ε^4* ε^4*	1 1	ε^4* ε^4*	-ε^7* -ε^7*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^5* -ε^5*	ε^6* ε^6*	ε^2* ε^2*	ε^2* ε^2*	ε^6* ε^6*	-ε^5* -ε^5*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^7* -ε^7*	ε^4* ε^4*	1 1	ε^4* ε^4*	-ε^7* -ε^7*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^5* -ε^5*	ε^6* ε^6*	ε^2* ε^2*	ε^2* ε^2*	ε^6* ε^6*	-ε^5* -ε^5*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^7* -ε^7*	ε^4* ε^4*	1 1	ε^4* ε^4*	-ε^7* -ε^7*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^5* -ε^5*	ε^6* ε^6*	ε^2* ε^2*	ε^2* ε^2*	ε^6* ε^6*	-ε^5* -ε^5*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^7* -ε^7*	ε^4* ε^4*
E_5g*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*
E_6g*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*
E_7g*	1 1	ε^7* ε^7*	-ε^* -ε^*	-ε^6* -ε^6*	ε^2* ε^2*	ε^5* ε^5*	-ε^3* -ε^3*	-ε^4* -ε^4*	ε^4* ε^4*	ε^3* ε^3*	-ε^5* -ε^5*	-ε^2* -ε^2*	ε^6* ε^6*	ε^* ε^*	-ε^7* -ε^7*	-1 -1	-ε^7* -ε^7*	ε^* ε^*	ε^6* ε^6*	-ε^2* -ε^2*	-ε^5* -ε^5*	ε^3* ε^3*	ε^4* ε^4*	-ε^4* -ε^4*	-ε^3* -ε^3*	ε^5* ε^5*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^* -ε^*	ε^7* ε^7*	1 1	ε^7* ε^7*	-ε^* -ε^*	-ε^6* -ε^6*	ε^2* ε^2*	ε^5* ε^5*	-ε^3* -ε^3*	-ε^4* -ε^4*	ε^4* ε^4*	ε^3* ε^3*	-ε^5* -ε^5*	-ε^2* -ε^2*	ε^6* ε^6*	ε^* ε^*	-ε^7* -ε^7*	-1 -1	-ε^7* -ε^7*	ε^* ε^*	ε^6* ε^6*	-ε^2* -ε^2*	-ε^5* -ε^5*	ε^3* ε^3*	ε^4* ε^4*	-ε^4* -ε^4*	-ε^3* -ε^3*	ε^5* ε^5*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^* -ε^*	ε^7* ε^7*
E_8g*	1 1	-ε^7* -ε^7*	-ε^* -ε^*	ε^6* ε^6*	ε^2* ε^2*	-ε^5* -ε^5*	-ε^3* -ε^3*	ε^4* ε^4*	ε^4* ε^4*	-ε^3* -ε^3*	-ε^5* -ε^5*	ε^2* ε^2*	ε^6* ε^6*	-ε^* -ε^*	-ε^7* -ε^7*	1 1	-ε^7* -ε^7*	-ε^* -ε^*	ε^6* ε^6*	ε^2* ε^2*	-ε^5* -ε^5*	-ε^3* -ε^3*	ε^4* ε^4*	ε^4* ε^4*	-ε^3* -ε^3*	-ε^5* -ε^5*	ε^2* ε^2*	ε^6* ε^6*	-ε^* -ε^*	-ε^7* -ε^7*	1 1	-ε^7* -ε^7*	-ε^* -ε^*	ε^6* ε^6*	ε^2* ε^2*	-ε^5* -ε^5*	-ε^3* -ε^3*	ε^4* ε^4*	ε^4* ε^4*	-ε^3* -ε^3*	-ε^5* -ε^5*	ε^2* ε^2*	ε^6* ε^6*	-ε^* -ε^*	-ε^7* -ε^7*	1 1	-ε^7* -ε^7*	-ε^* -ε^*	ε^6* ε^6*	ε^2* ε^2*	-ε^5* -ε^5*	-ε^3* -ε^3*	ε^4* ε^4*	ε^4* ε^4*	-ε^3* -ε^3*	-ε^5* -ε^5*	ε^2* ε^2*	ε^6* ε^6*	-ε^* -ε^*	-ε^7* -ε^7*
E_9g*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*
E_10g*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*
E_11g*	1 1	-ε^4* -ε^4*	-ε^7* -ε^7*	ε^3* ε^3*	-ε^* -ε^*	ε^5* ε^5*	ε^6* ε^6*	-ε^2* -ε^2*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^5* -ε^5*	ε^* ε^*	-ε^3* -ε^3*	ε^7* ε^7*	ε^4* ε^4*	-1 -1	ε^4* ε^4*	ε^7* ε^7*	-ε^3* -ε^3*	ε^* ε^*	-ε^5* -ε^5*	-ε^6* -ε^6*	ε^2* ε^2*	-ε^2* -ε^2*	ε^6* ε^6*	ε^5* ε^5*	-ε^* -ε^*	ε^3* ε^3*	-ε^7* -ε^7*	-ε^4* -ε^4*	1 1	-ε^4* -ε^4*	-ε^7* -ε^7*	ε^3* ε^3*	-ε^* -ε^*	ε^5* ε^5*	ε^6* ε^6*	-ε^2* -ε^2*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^5* -ε^5*	ε^* ε^*	-ε^3* -ε^3*	ε^7* ε^7*	ε^4* ε^4*	-1 -1	ε^4* ε^4*	ε^7* ε^7*	-ε^3* -ε^3*	ε^* ε^*	-ε^5* -ε^5*	-ε^6* -ε^6*	ε^2* ε^2*	-ε^2* -ε^2*	ε^6* ε^6*	ε^5* ε^5*	-ε^* -ε^*	ε^3* ε^3*	-ε^7* -ε^7*	-ε^4* -ε^4*
E_12g*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*
E_13g*	1 1	-ε^2* -ε^2*	ε^4* ε^4*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^5* ε^5*	-ε^3* -ε^3*	ε^* ε^*	-ε^* -ε^*	ε^3* ε^3*	-ε^5* -ε^5*	ε^7* ε^7*	ε^6* ε^6*	-ε^4* -ε^4*	ε^2* ε^2*	-1 -1	ε^2* ε^2*	-ε^4* -ε^4*	ε^6* ε^6*	ε^7* ε^7*	-ε^5* -ε^5*	ε^3* ε^3*	-ε^* -ε^*	ε^* ε^*	-ε^3* -ε^3*	ε^5* ε^5*	-ε^7* -ε^7*	-ε^6* -ε^6*	ε^4* ε^4*	-ε^2* -ε^2*	1 1	-ε^2* -ε^2*	ε^4* ε^4*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^5* ε^5*	-ε^3* -ε^3*	ε^* ε^*	-ε^* -ε^*	ε^3* ε^3*	-ε^5* -ε^5*	ε^7* ε^7*	ε^6* ε^6*	-ε^4* -ε^4*	ε^2* ε^2*	-1 -1	ε^2* ε^2*	-ε^4* -ε^4*	ε^6* ε^6*	ε^7* ε^7*	-ε^5* -ε^5*	ε^3* ε^3*	-ε^* -ε^*	ε^* ε^*	-ε^3* -ε^3*	ε^5* ε^5*	-ε^7* -ε^7*	-ε^6* -ε^6*	ε^4* ε^4*	-ε^2* -ε^2*
E_14g*	1 1	-ε^* -ε^*	ε^2* ε^2*	-ε^3* -ε^3*	ε^4* ε^4*	-ε^5* -ε^5*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^7* -ε^7*	ε^6* ε^6*	-ε^5* -ε^5*	ε^4* ε^4*	-ε^3* -ε^3*	ε^2* ε^2*	-ε^* -ε^*	1 1	-ε^* -ε^*	ε^2* ε^2*	-ε^3* -ε^3*	ε^4* ε^4*	-ε^5* -ε^5*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^7* -ε^7*	ε^6* ε^6*	-ε^5* -ε^5*	ε^4* ε^4*	-ε^3* -ε^3*	ε^2* ε^2*	-ε^* -ε^*	1 1	-ε^* -ε^*	ε^2* ε^2*	-ε^3* -ε^3*	ε^4* ε^4*	-ε^5* -ε^5*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^7* -ε^7*	ε^6* ε^6*	-ε^5* -ε^5*	ε^4* ε^4*	-ε^3* -ε^3*	ε^2* ε^2*	-ε^* -ε^*	1 1	-ε^* -ε^*	ε^2* ε^2*	-ε^3* -ε^3*	ε^4* ε^4*	-ε^5* -ε^5*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^7* -ε^7*	ε^6* ε^6*	-ε^5* -ε^5*	ε^4* ε^4*	-ε^3* -ε^3*	ε^2* ε^2*	-ε^* -ε^*
A_u	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1	-1
B_u	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1	1
E_1u*	1 1	ε^* ε^*	ε^2* ε^2*	ε^3* ε^3*	ε^4* ε^4*	ε^5* ε^5*	ε^6* ε^6*	ε^7* ε^7*	-ε^7* -ε^7*	-ε^6* -ε^6*	-ε^5* -ε^5*	-ε^4* -ε^4*	-ε^3* -ε^3*	-ε^2* -ε^2*	-ε^* -ε^*	-1 -1	-ε^* -ε^*	-ε^2* -ε^2*	-ε^3* -ε^3*	-ε^4* -ε^4*	-ε^5* -ε^5*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^7* ε^7*	ε^6* ε^6*	ε^5* ε^5*	ε^4* ε^4*	ε^3* ε^3*	ε^2* ε^2*	ε^* ε^*	-1 -1	-ε^* -ε^*	-ε^2* -ε^2*	-ε^3* -ε^3*	-ε^4* -ε^4*	-ε^5* -ε^5*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^7* ε^7*	ε^6* ε^6*	ε^5* ε^5*	ε^4* ε^4*	ε^3* ε^3*	ε^2* ε^2*	ε^* ε^*	1 1	ε^* ε^*	ε^2* ε^2*	ε^3* ε^3*	ε^4* ε^4*	ε^5* ε^5*	ε^6* ε^6*	ε^7* ε^7*	-ε^7* -ε^7*	-ε^6* -ε^6*	-ε^5* -ε^5*	-ε^4* -ε^4*	-ε^3* -ε^3*	-ε^2* -ε^2*	-ε^* -ε^*
E_2u*	1 1	ε^2* ε^2*	ε^4* ε^4*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^5* -ε^5*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^5* -ε^5*	-ε^7* -ε^7*	ε^6* ε^6*	ε^4* ε^4*	ε^2* ε^2*	1 1	ε^2* ε^2*	ε^4* ε^4*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^5* -ε^5*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^5* -ε^5*	-ε^7* -ε^7*	ε^6* ε^6*	ε^4* ε^4*	ε^2* ε^2*	-1 -1	-ε^2* -ε^2*	-ε^4* -ε^4*	-ε^6* -ε^6*	ε^7* ε^7*	ε^5* ε^5*	ε^3* ε^3*	ε^* ε^*	ε^* ε^*	ε^3* ε^3*	ε^5* ε^5*	ε^7* ε^7*	-ε^6* -ε^6*	-ε^4* -ε^4*	-ε^2* -ε^2*	-1 -1	-ε^2* -ε^2*	-ε^4* -ε^4*	-ε^6* -ε^6*	ε^7* ε^7*	ε^5* ε^5*	ε^3* ε^3*	ε^* ε^*	ε^* ε^*	ε^3* ε^3*	ε^5* ε^5*	ε^7* ε^7*	-ε^6* -ε^6*	-ε^4* -ε^4*	-ε^2* -ε^2*
E_3u*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*	-1 -1	-ε^3* -ε^3*	-ε^6* -ε^6*	ε^6* ε^6*	ε^3* ε^3*	1 1	ε^3* ε^3*	ε^6* ε^6*	-ε^6* -ε^6*	-ε^3* -ε^3*
E_4u*	1 1	ε^4* ε^4*	-ε^7* -ε^7*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^5* -ε^5*	ε^6* ε^6*	ε^2* ε^2*	ε^2* ε^2*	ε^6* ε^6*	-ε^5* -ε^5*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^7* -ε^7*	ε^4* ε^4*	1 1	ε^4* ε^4*	-ε^7* -ε^7*	-ε^3* -ε^3*	-ε^* -ε^*	-ε^5* -ε^5*	ε^6* ε^6*	ε^2* ε^2*	ε^2* ε^2*	ε^6* ε^6*	-ε^5* -ε^5*	-ε^* -ε^*	-ε^3* -ε^3*	-ε^7* -ε^7*	ε^4* ε^4*	-1 -1	-ε^4* -ε^4*	ε^7* ε^7*	ε^3* ε^3*	ε^* ε^*	ε^5* ε^5*	-ε^6* -ε^6*	-ε^2* -ε^2*	-ε^2* -ε^2*	-ε^6* -ε^6*	ε^5* ε^5*	ε^* ε^*	ε^3* ε^3*	ε^7* ε^7*	-ε^4* -ε^4*	-1 -1	-ε^4* -ε^4*	ε^7* ε^7*	ε^3* ε^3*	ε^* ε^*	ε^5* ε^5*	-ε^6* -ε^6*	-ε^2* -ε^2*	-ε^2* -ε^2*	-ε^6* -ε^6*	ε^5* ε^5*	ε^* ε^*	ε^3* ε^3*	ε^7* ε^7*	-ε^4* -ε^4*
E_5u*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*	-1 -1	-ε^5* -ε^5*	ε^5* ε^5*	1 1	ε^5* ε^5*	-ε^5* -ε^5*
E_6u*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	1 1	ε^6* ε^6*	-ε^3* -ε^3*	-ε^3* -ε^3*	ε^6* ε^6*	-1 -1	-ε^6* -ε^6*	ε^3* ε^3*	ε^3* ε^3*	-ε^6* -ε^6*	-1 -1	-ε^6* -ε^6*	ε^3* ε^3*	ε^3* ε^3*	-ε^6* -ε^6*	-1 -1	-ε^6* -ε^6*	ε^3* ε^3*	ε^3* ε^3*	-ε^6* -ε^6*	-1 -1	-ε^6* -ε^6*	ε^3* ε^3*	ε^3* ε^3*	-ε^6* -ε^6*	-1 -1	-ε^6* -ε^6*	ε^3* ε^3*	ε^3* ε^3*	-ε^6* -ε^6*	-1 -1	-ε^6* -ε^6*	ε^3* ε^3*	ε^3* ε^3*	-ε^6* -ε^6*
E_7u*	1 1	ε^7* ε^7*	-ε^* -ε^*	-ε^6* -ε^6*	ε^2* ε^2*	ε^5* ε^5*	-ε^3* -ε^3*	-ε^4* -ε^4*	ε^4* ε^4*	ε^3* ε^3*	-ε^5* -ε^5*	-ε^2* -ε^2*	ε^6* ε^6*	ε^* ε^*	-ε^7* -ε^7*	-1 -1	-ε^7* -ε^7*	ε^* ε^*	ε^6* ε^6*	-ε^2* -ε^2*	-ε^5* -ε^5*	ε^3* ε^3*	ε^4* ε^4*	-ε^4* -ε^4*	-ε^3* -ε^3*	ε^5* ε^5*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^* -ε^*	ε^7* ε^7*	-1 -1	-ε^7* -ε^7*	ε^* ε^*	ε^6* ε^6*	-ε^2* -ε^2*	-ε^5* -ε^5*	ε^3* ε^3*	ε^4* ε^4*	-ε^4* -ε^4*	-ε^3* -ε^3*	ε^5* ε^5*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^* -ε^*	ε^7* ε^7*	1 1	ε^7* ε^7*	-ε^* -ε^*	-ε^6* -ε^6*	ε^2* ε^2*	ε^5* ε^5*	-ε^3* -ε^3*	-ε^4* -ε^4*	ε^4* ε^4*	ε^3* ε^3*	-ε^5* -ε^5*	-ε^2* -ε^2*	ε^6* ε^6*	ε^* ε^*	-ε^7* -ε^7*
E_8u*	1 1	-ε^7* -ε^7*	-ε^* -ε^*	ε^6* ε^6*	ε^2* ε^2*	-ε^5* -ε^5*	-ε^3* -ε^3*	ε^4* ε^4*	ε^4* ε^4*	-ε^3* -ε^3*	-ε^5* -ε^5*	ε^2* ε^2*	ε^6* ε^6*	-ε^* -ε^*	-ε^7* -ε^7*	1 1	-ε^7* -ε^7*	-ε^* -ε^*	ε^6* ε^6*	ε^2* ε^2*	-ε^5* -ε^5*	-ε^3* -ε^3*	ε^4* ε^4*	ε^4* ε^4*	-ε^3* -ε^3*	-ε^5* -ε^5*	ε^2* ε^2*	ε^6* ε^6*	-ε^* -ε^*	-ε^7* -ε^7*	-1 -1	ε^7* ε^7*	ε^* ε^*	-ε^6* -ε^6*	-ε^2* -ε^2*	ε^5* ε^5*	ε^3* ε^3*	-ε^4* -ε^4*	-ε^4* -ε^4*	ε^3* ε^3*	ε^5* ε^5*	-ε^2* -ε^2*	-ε^6* -ε^6*	ε^* ε^*	ε^7* ε^7*	-1 -1	ε^7* ε^7*	ε^* ε^*	-ε^6* -ε^6*	-ε^2* -ε^2*	ε^5* ε^5*	ε^3* ε^3*	-ε^4* -ε^4*	-ε^4* -ε^4*	ε^3* ε^3*	ε^5* ε^5*	-ε^2* -ε^2*	-ε^6* -ε^6*	ε^* ε^*	ε^7* ε^7*
E_9u*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*	-1 -1	ε^6* ε^6*	ε^3* ε^3*	-ε^3* -ε^3*	-ε^6* -ε^6*	1 1	-ε^6* -ε^6*	-ε^3* -ε^3*	ε^3* ε^3*	ε^6* ε^6*
E_10u*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	1 1	-ε^5* -ε^5*	-ε^5* -ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*	-1 -1	ε^5* ε^5*	ε^5* ε^5*
E_11u*	1 1	-ε^4* -ε^4*	-ε^7* -ε^7*	ε^3* ε^3*	-ε^* -ε^*	ε^5* ε^5*	ε^6* ε^6*	-ε^2* -ε^2*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^5* -ε^5*	ε^* ε^*	-ε^3* -ε^3*	ε^7* ε^7*	ε^4* ε^4*	-1 -1	ε^4* ε^4*	ε^7* ε^7*	-ε^3* -ε^3*	ε^* ε^*	-ε^5* -ε^5*	-ε^6* -ε^6*	ε^2* ε^2*	-ε^2* -ε^2*	ε^6* ε^6*	ε^5* ε^5*	-ε^* -ε^*	ε^3* ε^3*	-ε^7* -ε^7*	-ε^4* -ε^4*	-1 -1	ε^4* ε^4*	ε^7* ε^7*	-ε^3* -ε^3*	ε^* ε^*	-ε^5* -ε^5*	-ε^6* -ε^6*	ε^2* ε^2*	-ε^2* -ε^2*	ε^6* ε^6*	ε^5* ε^5*	-ε^* -ε^*	ε^3* ε^3*	-ε^7* -ε^7*	-ε^4* -ε^4*	1 1	-ε^4* -ε^4*	-ε^7* -ε^7*	ε^3* ε^3*	-ε^* -ε^*	ε^5* ε^5*	ε^6* ε^6*	-ε^2* -ε^2*	ε^2* ε^2*	-ε^6* -ε^6*	-ε^5* -ε^5*	ε^* ε^*	-ε^3* -ε^3*	ε^7* ε^7*	ε^4* ε^4*
E_12u*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	1 1	-ε^3* -ε^3*	ε^6* ε^6*	ε^6* ε^6*	-ε^3* -ε^3*	-1 -1	ε^3* ε^3*	-ε^6* -ε^6*	-ε^6* -ε^6*	ε^3* ε^3*	-1 -1	ε^3* ε^3*	-ε^6* -ε^6*	-ε^6* -ε^6*	ε^3* ε^3*	-1 -1	ε^3* ε^3*	-ε^6* -ε^6*	-ε^6* -ε^6*	ε^3* ε^3*	-1 -1	ε^3* ε^3*	-ε^6* -ε^6*	-ε^6* -ε^6*	ε^3* ε^3*	-1 -1	ε^3* ε^3*	-ε^6* -ε^6*	-ε^6* -ε^6*	ε^3* ε^3*	-1 -1	ε^3* ε^3*	-ε^6* -ε^6*	-ε^6* -ε^6*	ε^3* ε^3*
E_13u*	1 1	-ε^2* -ε^2*	ε^4* ε^4*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^5* ε^5*	-ε^3* -ε^3*	ε^* ε^*	-ε^* -ε^*	ε^3* ε^3*	-ε^5* -ε^5*	ε^7* ε^7*	ε^6* ε^6*	-ε^4* -ε^4*	ε^2* ε^2*	-1 -1	ε^2* ε^2*	-ε^4* -ε^4*	ε^6* ε^6*	ε^7* ε^7*	-ε^5* -ε^5*	ε^3* ε^3*	-ε^* -ε^*	ε^* ε^*	-ε^3* -ε^3*	ε^5* ε^5*	-ε^7* -ε^7*	-ε^6* -ε^6*	ε^4* ε^4*	-ε^2* -ε^2*	-1 -1	ε^2* ε^2*	-ε^4* -ε^4*	ε^6* ε^6*	ε^7* ε^7*	-ε^5* -ε^5*	ε^3* ε^3*	-ε^* -ε^*	ε^* ε^*	-ε^3* -ε^3*	ε^5* ε^5*	-ε^7* -ε^7*	-ε^6* -ε^6*	ε^4* ε^4*	-ε^2* -ε^2*	1 1	-ε^2* -ε^2*	ε^4* ε^4*	-ε^6* -ε^6*	-ε^7* -ε^7*	ε^5* ε^5*	-ε^3* -ε^3*	ε^* ε^*	-ε^* -ε^*	ε^3* ε^3*	-ε^5* -ε^5*	ε^7* ε^7*	ε^6* ε^6*	-ε^4* -ε^4*	ε^2* ε^2*
E_14u*	1 1	-ε^* -ε^*	ε^2* ε^2*	-ε^3* -ε^3*	ε^4* ε^4*	-ε^5* -ε^5*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^7* -ε^7*	ε^6* ε^6*	-ε^5* -ε^5*	ε^4* ε^4*	-ε^3* -ε^3*	ε^2* ε^2*	-ε^* -ε^*	1 1	-ε^* -ε^*	ε^2* ε^2*	-ε^3* -ε^3*	ε^4* ε^4*	-ε^5* -ε^5*	ε^6* ε^6*	-ε^7* -ε^7*	-ε^7* -ε^7*	ε^6* ε^6*	-ε^5* -ε^5*	ε^4* ε^4*	-ε^3* -ε^3*	ε^2* ε^2*	-ε^* -ε^*	-1 -1	ε^* ε^*	-ε^2* -ε^2*	ε^3* ε^3*	-ε^4* -ε^4*	ε^5* ε^5*	-ε^6* -ε^6*	ε^7* ε^7*	ε^7* ε^7*	-ε^6* -ε^6*	ε^5* ε^5*	-ε^4* -ε^4*	ε^3* ε^3*	-ε^2* -ε^2*	ε^* ε^*	-1 -1	ε^* ε^*	-ε^2* -ε^2*	ε^3* ε^3*	-ε^4* -ε^4*	ε^5* ε^5*	-ε^6* -ε^6*	ε^7* ε^7*	ε^7* ε^7*	-ε^6* -ε^6*	ε^5* ε^5*	-ε^4* -ε^4*	ε^3* ε^3*	-ε^2* -ε^2*	ε^* ε^*

Number of symmetry elements	h = 60
Number of classes, irreps	n = 60
Number of real-valued irreducible representations	n = 32
Abelian group	yes
Optical Isomerism (Chirality)	no
Polar	no
Parity	yes

Point Group C_30h

Additional information

Reduce representation to irreducible representations

Genrate representation from irreducible representations

Direct products of irreducible representations

Error: Reduction failed