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D3×#64874 #14294547

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productD3×#64874

Splittings

FittingC3×C5×C4⋊C4 ⋊ C2×C4
HallC3×C5 ⋊ C2×#340
SylowC5 ⋊ D3×#340
SylowC3 ⋊ C2×#64874

Subgroups

subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#340
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#106
maximal normal subgroup ofD3×AGL(1,𝔽5)×#106

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20245);