C₂×#9743 #205186

order	512
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1806 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)(8,13)(9,14)(10,11)(15,16,17,20,18,21,22,19);(3,4,5,6)(7,8,11,9,12,14,10,13)(16,19)(17,22)(20,21);(7,9,11,14,12,13,10,8)

maximal subgroup of	C₂×#211236, C₂×#220728, C₂×#231631
maximal normal subgroup of	C₂×#211236, C₂×#220728, C₂×#231631

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 112382);