C₂×#7912 #181005

order	512
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

2226 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);(7,8,9,12,10,11,13,14)(15,16,18,20,19,21,17,22);(3,4,5,6)(8,11)(9,13);(8,11)(12,14)(15,17,19,18)(16,20,21,22)

maximal subgroup of	C₂×#232283, C₂×#195225, C₂×#196022, …
maximal normal subgroup of	C₂×#232283, C₂×#195225, C₂×#196022, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88201);