C₂×C₈×C₂²⋊Q₈ #6373114

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×C₈×C₂²⋊Q₈

2934 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);(3,4,5,6,7,8,9,10);(12,14)(15,16,18,20)(17,21,22,19);(15,17,18,22)(16,19,20,21);(11,12)(13,14)(15,16)(17,19)(18,20)(21,22)

maximal subgroup of	C₂×C₈×#525, C₂×D₈×C₂²⋊Q₈, C₂×#6578130, …
maximal normal subgroup of	C₂×C₈×#525, C₂×D₈×C₂²⋊Q₈, C₂×#6578130, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280310);