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D3×#65727 #14413393

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

Aliases

direct productD3×#65727

Splittings

FittingC3×C5×M16 ⋊ C2×C4
HallC3×C5 ⋊ C2×#428
SylowC5 ⋊ D3×#428
SylowC3 ⋊ C2×#65727

Subgroups

subgroupG/H
centerC2C2×D3×C4⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×M16C2×C4
socleC2×C3×C5C22×C4⋊C4
prime radicalC22×D3×D5D4
cosocleC3×C4×D5C24
hypercenterM16D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#428
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

1072 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×#10604003, #72230439, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), D3×#10604003, D3×#10603925
maximal quotient of#72230439, D3×#13103962

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 139091);