C₂×#14005 #514298

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

5050 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 5 generators on 18 points:

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

maximal subgroup of	C₂×#772920, C₂×#652612, C₂×#652047, …
maximal normal subgroup of	C₂×#772920, C₂×#652612, C₂×#652047, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421494);