C₂×#11466 #480073

order	512
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

1226 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	C₂×#480075, C₂×#130722
maximal normal subgroup of	C₂×#480075, C₂×#130722

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387269);