Finite Group Databasebeta

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C3×D3×D4×AGL(1,𝔽5) #72229964

order2880
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×D3×D4×AGL(1,𝔽5)

Splittings

FittingC32×C5×D4 ⋊ C2×C4
HallC32×C5 ⋊ C2×C4×D4
SylowC32 ⋊ C2×D4×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×D3×D4

Subgroups

subgroupG/H
centerC2×C3C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C23×C3×C4
FrattiniC2C22×C3×D3×AGL(1,𝔽5)
FittingC32×C5×D4C2×C4
socleC2×C32×C5C23×C4
prime radicalC3×D3×D4×D5C2
cosocleC2×C3×D5C24×C3
hypercenterC3×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C3×C4×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×D4

1798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×D4×AGL(1,𝔽5), D4×AGL(1,𝔽5)×AGL(1,ℤ/9), C3×D3×#11717375, …
maximal normal subgroup ofD32×D4×AGL(1,𝔽5), C3×AGL(1,𝔽5)×#1004, AGL(1,𝔽5)×#64314
maximal quotient ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9), C3×D3×#11717375, C3×AGL(1,𝔽5)×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.