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C₃×D₅×D₈ #91627

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₃×D₅×D₈

Splittings

Fitting	C₃×C₅×D₈ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×D₈
Sylow	C₅ ⋊ C₂×C₃×D₈

Subgroups

	subgroup	G/H
center	C₂×C₃	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×D₈	C₂
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₃×D₈	D₅
hypocenter	C₅	C₂×C₃×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

(2,5)(3,8)(6,7)(9,10,12,13,11)(14,15,16);(1,2)(3,5)(4,7)(6,8);(10,11)(12,13)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#64904, C₃×#64906, #11746775, …
maximal normal subgroup of	C₃×#64904, C₃×#64906, #11746775, …
maximal quotient of	C₃×#65045, C₃×#65048, C₃×#65049, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 703);