C₂²×C₄×#108 #6369922

order	512
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

C₂²×C₄×#108

3354 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 24 points:

(1,2);(3,4);(5,6,7,8);(9,10,13,16,14,17,12,22)(11,18,20,23,21,24,19,15);(9,11,12,19,14,21,13,20)(10,15,16,18,17,23,22,24)

maximal subgroup of	C₂²×C₄×#365, C₂²×C₄×#444, C₂²×C₄×#361, …
maximal normal subgroup of	C₂²×C₄×#365, C₂²×C₄×#444, C₂²×C₄×#361, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277118);