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D3×C4⋊C4×AGL(1,𝔽5) #14319475

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD3×C4⋊C4×AGL(1,𝔽5)

Splittings

FittingC3×C5×C4⋊C4 ⋊ C2×C4
HallC3×C5 ⋊ C2×C4×C4⋊C4
SylowC5 ⋊ C4×D3×C4⋊C4
SylowC3 ⋊ C2×C4⋊C4×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C23×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45173);