C₂×#9653 #204173

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

Aliases

2970 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)(15,16,19,21,18,20,22,17);(7,9)(8,11,12,14)(10,13)(15,17,19,20,18,21,22,16);(3,4,5,6)(8,12)(11,14)(16,20)(17,21)

maximal subgroup of	C₂×#258131, C₂×#204176, C₂×#261347, …
maximal normal subgroup of	C₂×#258131, C₂×#204176, C₂×#261347, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 111369);