C₂×#8949 #193550

order	512
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1644 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 22 points:

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

maximal subgroup of	C₂×#249471, C₂×#249535, C₂×#193646, …
maximal normal subgroup of	C₂×#249471, C₂×#249535, C₂×#193646, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 100746);