C₅×C₃²⋊C₂₇ #11925938

order	1215
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₂₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₅×C₃²⋊C₂₇
unambiguous semidirect product	C₃²⋊(C₅×C₂₇)
unambiguous semidirect product	(C₃²×C₅)⋊C₂₇

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 405

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

(1,2,3,4,5)(6,7,9)(8,11,13)(10,14,12)(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);(7,10,11)(9,13,14)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1215, 12);