C₃³×C₅×C₉ #11925987

order	1215
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 196515072
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃⁶

Aliases

C₃³×C₅×C₉

792 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 1215

A minimal faithful permutation representation — 4 generators on 23 points:

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

1215 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 61);