C₂×#10734 #353402

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

4678 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)(5,6)(7,8,9,10)(11,12,14,19,16,20,15,18)(13,21,23,26,24,25,22,17);(11,13,15,22,16,24,14,23)(12,17,18,25,20,26,19,21);(4,6)

maximal subgroup of	C₂×#360188, C₂×#354818, C₂×#366295
maximal normal subgroup of	C₂×#360188, C₂×#354818, C₂×#366295

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260598);