C₂×#10968 #357425

order	512
nilpotency class	3
isoclinism	isoclinic class of #8304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

5042 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)(11,12,14,18,15,17,23,25)(13,19,20,26,21,16,22,24);(7,8)(9,10)(11,13,15,21)(12,16,17,19)(14,22,23,20)(18,26,25,24);(4,6)(8,10)

maximal subgroup of	C₂×#357426, #72317090, C₂×#394095
maximal normal subgroup of	C₂×#357426, #72317090, C₂×#394095

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264621);