C₂×#9081 #195919

order	512
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁸

Aliases

3134 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 22 points:

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

maximal subgroup of	C₂×#255122, C₂×#257042, C₂×#246039, …
maximal normal subgroup of	C₂×#255122, C₂×#257042, C₂×#246039, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 103115);