C₉×C₁₁⋊C₁₆ #13096838

order	1584
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₁⋊C₁₆
unambiguous semidirect product	C₁₁⋊(C₉×C₁₆)

derived, Sylow	C₁₁ ⋊ C₉×C₁₆
Hall	C₉×C₁₁ ⋊ C₁₆

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1584

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5,6,7,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22,23,26,24,27,29,32,25,28,30,33,31,34,35,36);(10,11,13,15,17,19,20,18,16,14,12)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 2);