C₂×#21834 #6374355

order	512
nilpotency class	3
isoclinism	isoclinic class of #3186
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁷×C₄²

Aliases

4474 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)(9,14)(10,13)(11,12)(16,19)(17,21)(20,22);(7,9,10,11)(8,12,13,14);(8,12)(9,11)(13,14)(15,16,18,20)(17,22,21,19);(8,13)(12,14)

maximal subgroup of	#72305015, #72305020, C₂×#6481495, …
maximal normal subgroup of	#72305015, #72305020, C₂×#6481495, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281551);