C₂×#7876 #180916

order	512
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1926 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)(15,16,17,20,18,19,21,22);(4,6)(7,8,10,14,11,13,9,12);(8,13)(12,14)(16,19)(20,22)

maximal subgroup of	C₂×#193640, C₂×#197807, C₂×#233136
maximal normal subgroup of	C₂×#193640, C₂×#197807, C₂×#233136

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88112);