C₅×C₉×C₂₇ #11925936

order	1215
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 34992
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉

Aliases

C₅×C₉×C₂₇

72 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1215

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)(37,38,39,40,41);(28,29,30,31,32,33,34,35,36)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 10);