C₂³×#391 #7625241

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

28018 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532437);