C₂×C₄×#455 #6372697

order	512
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

4924 conjugacy classes of subgroups.

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

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

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

maximal subgroup of	C₂×C₄×#3019, #72312715, C₄×#33558, …
maximal normal subgroup of	C₂×C₄×#3019, #72312715, C₄×#33558, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279893);