C₂×#13202 #495113

order	512
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1734 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 26 points:

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

maximal subgroup of	C₂×#496104, C₂×#498306, C₂×D₄×#357
maximal normal subgroup of	C₂×#496104, C₂×#498306, C₂×D₄×#357

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402309);