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D3×#65767 #14412415

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productD3×#65767

Splittings

FittingC2×C3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ C2×#418
SylowC5 ⋊ D3×#418
SylowC3 ⋊ C2×#65767

Subgroups

subgroupG/H
centerC2C2×D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×D3×D4×D5C2
cosocleC3×C4×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#418
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

2016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), D3×#10604863, #72230450, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), D3×#10604863, D3×#10604614
maximal quotient of#72230450, D3×#13104909

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138113);