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C₃×#3996 #91200

order	480
isoclinism	isoclinic class of #3993
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅ ⋊ #108
Sylow	C₅ ⋊ C₃×#108

Subgroups

	subgroup	G/H
center	C₂×C₃	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₄	C₂×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×C₈	C₄
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂×C₃×D₅	Q₈
cosocle	C₄×D₅	C₂²×C₃
hypercenter	C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#108
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

60 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:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746460, #11746461, #11746478, …
maximal normal subgroup of	#11746460, #11746461, #11746478, …
maximal quotient of	C₃×#64882, C₃×#64883, C₃×#64896, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 276);