C₂×#13252 #495247

order	512
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1694 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)(8,10)(11,12,13,17,21,25,26,24,15,19,22,23,14,18,20,16);(3,4,5,6)(12,16)(13,20)(14,21)(17,18)(19,24)(22,26)(23,25);(7,8,9,10)

maximal subgroup of	C₂×#495812, C₂×#498562, C₂×D₄×#357
maximal normal subgroup of	C₂×#495812, C₂×#498562, C₂×D₄×#357

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402443);