C₂×#11023 #357508

order	512
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

5598 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 22 points:

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

maximal subgroup of	C₂×#357515, #72317115, C₂×#359488, …
maximal normal subgroup of	C₂×#357515, #72317115, C₂×#359488, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264704);