C₃×C₉×Dic₁₁ #11924641

order	1188
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₉×Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₃×C₄×C₉)

derived, Sylow	C₁₁ ⋊ C₃×C₄×C₉
Hall	C₃×C₉×C₁₁ ⋊ C₄

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1188

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 11);