C₂×#8573 #188433

order	512
nilpotency class	3
isoclinism	isoclinic class of #7606
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1998 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	C₂×#265779, C₂×#188484, C₂×#258135, …
maximal normal subgroup of	C₂×#265779, C₂×#188484, C₂×#258135, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 95629);