C₂×#7263 #127523

order	512
nilpotency class	4
isoclinism	isoclinic class of #7262
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

886 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)(12,16,17,24)(13,20)(14,23)(18,21,19,25)(22,26);(4,7,9,8)(11,12,14,18,15,17,23,19)(13,21,20,16,22,25,26,24)

maximal subgroup of	C₂×#127647, C₂×#128808, C₂×#128836
maximal normal subgroup of	C₂×#127647, C₂×#128808, C₂×#128836

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 34719);