C₉×Dic₄₄ #13096871

order	1584
isoclinism	isoclinic class of #4314
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×Dic₄₄

Splittings

Hall	C₉×C₁₁ ⋊ Q₁₆
Sylow	C₁₁ ⋊ C₉×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₉	D₄₄
commutator	C₄×C₁₁	C₂²×C₉
Frattini	C₃×C₄	C₂×C₃×D₁₁
Fitting	C₈×C₉×C₁₁	C₂
socle, prime radical	C₂×C₃×C₁₁	C₃×D₄
cosocle	C₃×C₄×C₁₁	C₂²×C₃
hypercenter	C₈×C₉	D₁₁
hypocenter	C₁₁	C₉×Q₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉ ◁ C₈×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)(10,11,12,13,14,15,16,17)(18,25,24,23,22,21,20,19)(26,27,28,29,30,31,32,33,34,35,36);(10,18,14,22)(11,19,15,23)(12,20,16,24)(13,21,17,25)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 35);

C9×Dic44 #13096871