Finite Group Databasebeta

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C₃×#64931 #11746708

order	960
isoclinism	isoclinic class of #64868
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Hall	C₃×C₅ ⋊ #333
Sylow	C₅ ⋊ C₃×#333

Subgroups

	subgroup	G/H
center	C₂²×C₃	C₂²⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×Q₈	C₄
socle, prime radical	C₂²×C₃×C₅	C₂²⋊C₄
cosocle	C₄×Dic₅	C₂²×C₃
hypercenter	C₂×C₃×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#333
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₈

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

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

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

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#10598836, C₃×#10598576, #14279384, …
maximal normal subgroup of	C₃×#10598836, C₃×#10598576, #14279384, …
maximal quotient of	C₃×#10598828, C₃×#10598715, C₃×#10598725, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 903);