C₂×#8611 #188832

order	512
nilpotency class	3
isoclinism	isoclinic class of #8608
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1346 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)(11,12,15,18,16,19,14,24)(13,20,22,25,23,26,21,17);(11,13,14,21,16,23,15,22)(12,17,18,20,19,25,24,26);(3,5)(4,7)(6,10)(8,9)

maximal subgroup of	C₂×#188834, C₂×#130722
maximal normal subgroup of	C₂×#188834, C₂×#130722

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 96028);