C₃×C₅×C₉⋊C₉ #11925959

order	1215
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅×C₉ · Schur multiplier (H₂) = C₃³

Aliases

C₃×C₅×C₉⋊C₉

180 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1215

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3)(22,23,24,25,26);(5,7,10)(8,12,11)(13,14,16,15,17,19,18,20,21);(4,5,8,6,7,11,9,10,12)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 33);