C₂²×#1950 #6371902

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

2858 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);(6,8)(9,10,13,16,14,17,12,21)(11,18,19,15,20,23,22,24);(9,11,13,19,14,20,12,22)(10,15,16,23,17,24,21,18);(5,6,7,8)

maximal subgroup of	C₂²×D₄×#108, C₂²×#23016, C₂²×#21518
maximal normal subgroup of	C₂²×D₄×#108, C₂²×#23016, C₂²×#21518

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279098);