C₉×#4326 #13096881

order	1584
isoclinism	isoclinic class of #4323
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×#4326

Splittings

Hall	C₉×C₁₁ ⋊ Q₁₆
Sylow	C₁₁ ⋊ C₉×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₉	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂²×C₉
Frattini	C₃×C₄	C₂×C₃×D₁₁
Fitting	Q₈×C₉×C₁₁	C₂
socle, prime radical	C₂×C₃×C₁₁	C₃×D₄
cosocle	C₃×C₄×C₁₁	C₂²×C₃
hypercenter	Q₈×C₉	D₁₁
hypocenter	C₁₁	C₉×Q₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉ ◁ Q₈×C₉

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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)(10,11,13,15,17,19,20,18,16,14,12)(21,23,25,31)(22,26,28,35)(24,33,34,30)(27,36,32,29);(11,12)(13,14)(15,16)(17,18)(19,20)(21,22,25,28)(23,29,31,36)(24,32,34,27)(26,33,35,30)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 45);

C9×#4326 #13096881