C₅×C₉⋊Dic₉ #13108142

order	1620
isoclinism	isoclinic class of C₉⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₉

Aliases

direct product	C₅×C₉⋊Dic₉
unambiguous semidirect product	C₉⋊(C₅×Dic₉)

derived, Sylow	C₉² ⋊ C₄×C₅
Hall	C₅×C₉² ⋊ C₄

138 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1620

A minimal faithful permutation representation — 3 generators on 27 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 48);