C₉×C₄⋊Dic₁₁ #13096876

order	1584
isoclinism	isoclinic class of Dic₂₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂

Aliases

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

Hall	C₉×C₁₁ ⋊ C₄⋊C₄
Sylow	C₁₁ ⋊ C₉×C₄⋊C₄

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1584

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 40);