C₂×#8216 #182600

order	512
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2038 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89796);