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C₃×#3959 #91029

order	480
isoclinism	isoclinic class of #3958
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅ ⋊ SD₃₂
Sylow	C₅ ⋊ C₃×SD₃₂

Subgroups

	subgroup	G/H
center	C₂×C₃	#686
commutator, cosocle	C₅×C₈	C₂²×C₃
Frattini	C₈	C₂×C₃×D₅
Fitting, prime radical	C₃×C₅×D₈	C₂
socle	C₂×C₃×C₅	D₈
hypercenter	C₃×D₈	D₅
hypocenter	C₅	C₃×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×D₈

52 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:

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

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#3959, #11748273, #11748274, …
maximal normal subgroup of	D₃×#3959, #11748273, #11748274, …
maximal quotient of	C₃×#64710, C₃×#64712, C₃×#64782, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 105);