C₂×C₄×#354 #493002

order	512
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1586 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	C₄×#33558, #72312731, C₂×#503196, …
maximal normal subgroup of	C₄×#33558, #72312731, C₂×#503196, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400198);