Point Group S11

Point Group S₁₁

ε=exp(2πi/5)
S₁₁	E	(C₁₁)²	(C₁₁)⁴	(C₁₁)⁶	(C₁₁)⁸	i	(S₁₁)⁷	(S₁₁)⁹	S₁	(S₁₁)²	(S₁₁)⁴
A_g	1	1	1	1	1	1	1	1	1	1	1
E_1g*	1 1	ε^* ε^*	ε^2* ε^2*	ε^2* ε^2*	ε^* ε^*	1 1	ε^* ε^*	ε^2* ε^2*	ε^2* ε^2*	ε^* ε^*	1 1
E_2g*	1 1	ε^2* ε^2*	ε^* ε^*	ε^* ε^*	ε^2* ε^2*	1 1	ε^2* ε^2*	ε^* ε^*	ε^* ε^*	ε^2* ε^2*	1 1
A_u	1	1	1	1	1	-1	-1	-1	-1	-1	-1
E_1u*	1 1	ε^* ε^*	ε^2* ε^2*	ε^2* ε^2*	ε^* ε^*	-1 -1	-ε^* -ε^*	-ε^2* -ε^2*	-ε^2* -ε^2*	-ε^* -ε^*	-1 -1
E_2u*	1 1	ε^2* ε^2*	ε^* ε^*	ε^* ε^*	ε^2* ε^2*	-1 -1	-ε^2* -ε^2*	-ε^* -ε^*	-ε^* -ε^*	-ε^2* -ε^2*	-1 -1

Additional information

Number of symmetry elements	h = 11
Number of classes, irreps	n = 11
Number of real-valued irreducible representations	n = 6
Abelian group	yes
Optical Isomerism (Chirality)	no
Polar	no
Parity	yes

Reduce representation to irreducible representations