C₂×#7017 #94954

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

Aliases

1450 conjugacy classes of subgroups.

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

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

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

maximal subgroup of	C₂×#94969, #72268637, #72268638
maximal normal subgroup of	C₂×#94969, #72268637, #72268638

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 2150);