C₂×#13761 #513345

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁷×C₄³

Aliases

7890 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);(4,6)(7,8,9,10)(15,16)(17,20)(18,19)(21,22);(11,12,13,14)(16,19)(20,22);(3,4,5,6)(8,10);(15,17,18,21)(16,20,19,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420541);