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D3×#65731 #14416527

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#65731

Splittings

FittingC3×C5×D8 ⋊ C2×C4
HallC3×C5 ⋊ C2×#442
SylowC5 ⋊ D3×#442
SylowC3 ⋊ C2×#65731

Subgroups

subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×D8C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD3×D5×D8C2
cosocleC3×C4×D5C24
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#442
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ D8

1216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), #72230444, D3×#13104056
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8)
maximal quotient of#72230444, D3×#13104056

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142225);