C₂×#10715 #353290

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

5338 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

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

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

maximal subgroup of	C₂×#353385, C₂×#359493, C₂×#354295, …
maximal normal subgroup of	C₂×#353385, C₂×#359493, C₂×#354295, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260486);