C₂×#11465 #480072

order	512
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₆ · Schur multiplier (H₂) = C₂⁷

Aliases

1270 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)(11,12,14,18,15,19,23,26,16,20,13,17,21,24,22,25);(3,5)(4,7)(6,10)(8,9);(11,13,15,22,16,14,21,23)(12,17,19,25,20,18,24,26)

maximal subgroup of	C₂×#480075, C₂×#130718
maximal normal subgroup of	C₂×#480075, C₂×#130718

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387268);