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C₅×#800 #91043

order	480
isoclinism	isoclinic class of D₄₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting	C₃×C₅×C₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ SD₃₂
Sylow	C₃ ⋊ C₅×SD₃₂

Subgroups

	subgroup	G/H
center	C₂×C₅	D₂₄
commutator, cosocle	C₃×C₈	C₂²×C₅
Frattini	C₈	C₂×C₅×D₃
Fitting	C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	D₈
prime radical	C₅×D₂₄	C₂
hypercenter	C₅×C₁₆	D₃
hypocenter	C₃	C₅×SD₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

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:

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

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×#800, #11746817, #11746823, …
maximal normal subgroup of	D₅×#800, #11746817, #11746823, …
maximal quotient of	C₅×#4503, C₅×#4505, C₅×#4509, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 119);