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C₃×#64686 #11746043

order	960
isoclinism	isoclinic class of #64686
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅ ⋊ #347
Sylow	C₅ ⋊ C₃×#347

Subgroups

	subgroup	G/H
center	C₃×C₄	C₄×Dic₅
commutator	C₄×C₅	C₃×C₄²
Frattini	C₂×C₈	C₂×C₃×D₅
Fitting	C₃×C₅×#97	C₂
socle	C₂×C₃×C₅	#97
prime radical	C₂²×C₃×C₅	M₁₆
cosocle	C₂×C₅×C₈	C₂²×C₃
hypercenter	C₃×#97	D₅
hypocenter	C₅	C₃×#347
LCS	G ▷ C₄×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₃×#97

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

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#10598011, C₃×#10598274, #14278360, …
maximal normal subgroup of	C₃×#10598011, C₃×#10598274, #14278360, …
maximal quotient of	C₃×#10597933, C₃×#10598154, C₂×C₃×#64686

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 238);