C₂×#7028 #96402

order	512
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

1554 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)(14,16)(15,18)(19,20,21,23,22,24,25,26);(4,7,9,8)(11,13)(12,15,16,17)(14,18)

maximal subgroup of	C₂×#96443, #72238899, #72238900, …
maximal normal subgroup of	C₂×#96443, #72238899, #72238900, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 3598);