C₂×#12811 #493755

order	512
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1414 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(4,6)(7,8,9,10)(11,12)(13,16)(14,23)(15,19)(17,20)(18,21)(22,25)(24,26);(3,4,5,6);(12,16)(13,20)(14,21)(17,18)(19,25)(22,26)(23,24)

maximal subgroup of	C₂×#495812, C₂×#497870, C₂×D₄×#357
maximal normal subgroup of	C₂×#495812, C₂×#497870, C₂×D₄×#357

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400951);