C₅×(C₃⋊Dic₃)⋊C₉ #13108117

order	1620
isoclinism	isoclinic class of (C₃⋊D₃)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×(C₃⋊Dic₃)⋊C₉
unambiguous semidirect product	(C₃⋊Dic₃)⋊(C₅×C₉)
unambiguous semidirect product	(C₅×C₃⋊Dic₃)⋊C₉

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5)(6,13,12,8,7,14,11,10,9)(16,21,23,18,19,22)(17,20)(24,25,26,27);(15,16,18)(17,19,22)(20,23,21)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 23);