C₂×#8019 #181499

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

3822 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);(3,4,5,6)(7,8)(9,11)(10,13)(12,14)(15,16)(17,21)(18,20)(19,22);(8,11,13,12)(15,17)(16,19,20,21)(18,22);(17,22)(19,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88695);