C₂×#7184 #126900

order	512
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂⁴

Aliases

1010 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 3 generators on 26 points:

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

maximal subgroup of	C₂×#126941, C₂×#128354, C₂×#128356, …
maximal normal subgroup of	C₂×#126941, C₂×#128354, C₂×#128356, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 34096);