C₂×#9652 #204172

order	512
nilpotency class	3
isoclinism	isoclinic class of #8304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

2078 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)(9,11,13,14)(10,12)(15,16,20,21,19,17,18,22);(7,9)(8,11,12,14)(10,13)(15,17,20,22,19,16,18,21);(3,4,5,6)(15,18,19,20)(16,21,17,22)

maximal subgroup of	C₂×#258135, C₂×#204176, C₂×#261403, …
maximal normal subgroup of	C₂×#258135, C₂×#204176, C₂×#261403, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 111368);