C₃×C₅×C₃²⋊C₉ #11925958

order	1215
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅×C₉ · Schur multiplier (H₂) = C₃⁴

Aliases

C₃×C₅×C₃²⋊C₉

288 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 405

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 32);