C₂×#8819 #191425

order	512
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₈

Aliases

1074 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 98621);