C₂×#22963 #6381717

order	512
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

2630 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 22 points:

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

maximal subgroup of	C₂×#7522896, C₂×#7518166, C₂×#6382319
maximal normal subgroup of	C₂×#7522896, C₂×#7518166, C₂×#6382319

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6288913);