C₂²×#2168 #7622567

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹

Aliases

2258 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)(9,10,12,16,13,11,18,19,14,17,21,24,22,20,15,23);(6,8);(9,11,12,19,13,17,18,24,14,20,21,23,22,10,15,16)

maximal subgroup of	C₂²×#33484, C₂²×#33912, C₂²×#33885, …
maximal normal subgroup of	C₂²×#33484, C₂²×#33912, C₂²×#33885, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529763);