C₂×#12653 #493091

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

1022 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);(3,4,5,6)(7,8,10,9);(4,6)(11,12,13,17,14,18,19,24,15,16,20,22,21,23,25,26);(7,9,10,8)(12,16)(17,22)(18,23)(24,26)

maximal subgroup of	C₂×#134362, C₂×#140388, C₂×#495812, …
maximal normal subgroup of	C₂×#134362, C₂×#140388, C₂×#495812, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400287);