C₂×C₄×#395 #514030

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

6562 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

maximal subgroup of	C₂×#772920, C₂×#779723, C₂×#609207, …
maximal normal subgroup of	C₂×#772920, C₂×#779723, C₂×#609207, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421226);