C₂×#21303 #6372170

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4754 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);(4,6)(7,8)(9,13)(10,11)(12,14)(15,16,18,21,19,17,20,22);(3,4,5,6)(8,11)(12,13)(15,17,18,22,19,16,20,21);(7,9,10,14)(8,12,11,13);(16,17)(21,22)

maximal subgroup of	C₂×#6445476, C₂×#193646, C₂×#233082, …
maximal normal subgroup of	C₂×#6445476, C₂×#193646, C₂×#233082, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279366);