C₂×#13177 #495049

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

Aliases

830 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₂×#495812, C₂×#498306, C₂×D₄×#367
maximal normal subgroup of	C₂×#495812, C₂×#498306, C₂×D₄×#367

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402245);