C₂×#33487 #7622674

order	512
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁸

Aliases

1790 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 26 points:

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

maximal subgroup of	C₂×#7622691, C₂×#7624130
maximal normal subgroup of	C₂×#7622691, C₂×#7624130

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529870);