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C₅×D₄₈ #91042

order	480
isoclinism	isoclinic class of D₄₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₅×D₄₈

Splittings

Fitting	C₃×C₅×C₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ D₁₆
Sylow	C₃ ⋊ C₅×D₁₆

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
hypercenter	C₅×C₁₆	D₃
hypocenter	C₃	C₅×D₁₆
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

56 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)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24);(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)(23,24)

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745818, #11745820, #11745822, …
maximal normal subgroup of	#11745818, #11745820, #11745822, …
maximal quotient of	C₅×D₉₆, C₅×#4449, C₅×Dic₄₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 118);