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C₃×#64764 #11746121

order	960
isoclinism	isoclinic class of #64757
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Hall	C₃×C₅ ⋊ #331
Sylow	C₅ ⋊ C₃×#331

Subgroups

	subgroup	G/H
center	C₂²×C₃	C₂²⋊Dic₅
commutator	C₂×C₄×C₅	C₂×C₃×C₄
Frattini	C₄²	C₂×C₃×D₅
Fitting, prime radical	C₃×C₅×#127	C₂
socle	C₂²×C₃×C₅	C₂²⋊C₄
cosocle	C₄²×C₅	C₂²×C₃
hypercenter	C₃×#127	D₅
hypocenter	C₅	C₃×#331
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#127

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 480

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

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

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#10598029, C₃×#10598261, #14279308, …
maximal normal subgroup of	C₃×#10598029, C₃×#10598261, #14279308, …
maximal quotient of	C₃×#10598130, C₃×#10598125, C₃×#10598282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 316);