C₂×#34313 #7625621

order	512
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

12382 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 6 generators on 18 points:

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

maximal subgroup of	C₂×#7677127, C₂×#7686452, C₂×#7693648, …
maximal normal subgroup of	C₂×#7677127, C₂×#7686452, C₂×#7693648, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532817);