C₂×#21349 #6372274

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

Aliases

3066 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)(9,12)(10,11)(13,14)(15,16,19,17,18,20,22,21);(4,6)(15,17,19,20,18,21,22,16);(8,11)(12,14);(7,9,10,13)(8,12,11,14)

maximal subgroup of	C₂×#204555, C₂×#183301, C₂×#188396, …
maximal normal subgroup of	C₂×#204555, C₂×#183301, C₂×#188396, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279470);