C₂×#8288 #183433

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

1002 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₂×#184300, C₂×#229938, C₂×#229850, …
maximal normal subgroup of	C₂×#184300, C₂×#229938, C₂×#229850, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 90629);