Finite Group Databasebeta

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C4×AGL(1,𝔽5)×C3⋊Dic3 #72231539

order2880
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C3×C43

Aliases

direct productC4×AGL(1,𝔽5)×C3⋊Dic3

Splittings

derived, HallC32×C5 ⋊ C43
SylowC32 ⋊ C42×AGL(1,𝔽5)
SylowC5 ⋊ C42×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C4C3⋊D3×AGL(1,𝔽5)
commutator, hypocenterC32×C5C43
FrattiniC22C2×C3⋊D3×AGL(1,𝔽5)
FittingC2×C32×C4×C5C2×C4
socleC22×C32×C5C22×C4
prime radical, cosocleC22×C32×D5C23
LCSG ▷ C32×C5
UCSC1 ◁ C2×C4

1548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 720

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC42×C3⋊D3×AGL(1,𝔽5), AGL(1,𝔽5)×#64149, #72231689, …
maximal normal subgroup ofC42×C3⋊D3×AGL(1,𝔽5), AGL(1,𝔽5)×#64149, #72231689, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.