C₂×#8212 #182444

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1490 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)(8,12)(9,10)(13,14)(15,16,19,17,18,20,22,21);(4,6)(7,8,10,14,11,13,9,12)(16,20)(17,21);(8,13)(12,14)(15,17,19,20,18,21,22,16)

maximal subgroup of	C₂×#184140, C₂×#227650, C₂×#227762, …
maximal normal subgroup of	C₂×#184140, C₂×#227650, C₂×#227762, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89640);