C₂×C₄×#432 #6369946

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

3674 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)(9,12)(10,11)(13,14)(15,16,17,20,18,19,21,22);(8,11)(12,14);(7,9,10,13)(8,12,11,14)(16,19)(20,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277142);