C₁₁×C₃⋊Dic₉ #11924652

order	1188
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₁×C₃⋊Dic₉
unambiguous semidirect product	C₃⋊(C₁₁×Dic₉)
unambiguous semidirect product	C₉⋊(C₁₁×Dic₃)

derived, Sylow	C₃×C₉ ⋊ C₄×C₁₁
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 — 3 generators on 27 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1188, 22);