C₅×C₉⋊C₂₇ #11925947

order	1215
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₂₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₉⋊C₂₇
unambiguous semidirect product	C₉⋊(C₅×C₂₇)
unambiguous semidirect product	(C₅×C₉)⋊C₂₇

52 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)(7,9,12)(10,14,13)(15,16,19,17,20,25,22,27,32,18,21,26,23,28,33,30,35,38,24,29,34,31,36,39,37,40,41);(6,7,10,8,9,13,11,12,14)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 21);