C₉×#3954 #13083783

order	1440
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₁

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₉×#3954

Splittings

Hall	C₅×C₉ ⋊ #108
Sylow	C₅ ⋊ C₉×#108

Subgroups

	subgroup	G/H
center	C₄×C₉	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₄×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₅
Fitting	C₅×C₉×M₁₆	C₂
socle	C₂×C₃×C₅	C₃×C₄⋊C₄
prime radical	C₂²×C₃×C₅	C₃×Q₈
cosocle	C₂×C₃×C₄×C₅	C₂²×C₃
hypercenter	C₉×M₁₆	D₅
hypocenter	C₅	C₉×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ C₉×M₁₆

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 100);

C9×#3954 #13083783