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C₅×#919 #91722

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Fitting	C₃×C₅×Q₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ #135
Sylow	C₃ ⋊ C₅×#135

Subgroups

	subgroup	G/H
center	C₂×C₅	D₃×D₄
commutator, cosocle	C₃×C₄	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₁₆	C₂
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₅×Q₁₆	D₃
hypocenter	C₃	C₅×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₁₆

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11748291, #11748297, #11748304, …
maximal normal subgroup of	#11748291, #11748297, #11748304, …
maximal quotient of	C₅×#4788, C₅×#4796, C₅×#4800, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 798);