Finite Group Databasebeta

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C₃×#64889 #11746666

order	960
isoclinism	isoclinic class of #3993
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅ ⋊ #364
Sylow	C₅ ⋊ C₃×#364

Subgroups

	subgroup	G/H
center	C₃×C₄	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₃×C₈
Frattini	C₂×C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₄⋊C₈
prime radical	C₂²×C₃×C₅	M₁₆
cosocle	C₂×#168	C₂²×C₃
hypercenter	C₂×C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#364
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#10598815, C₃×#10598623, #14277906, …
maximal normal subgroup of	C₃×#10598815, C₃×#10598623, #14277906, …
maximal quotient of	C₃×#10598522, C₃×#10598524, C₃×#10598779, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 861);