C₇²×C₉ #89206

order	441
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 12096
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₇²×C₉

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 441

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16);(17,18,19,20,21,22,23)

441 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(441, 8);