Finite Group Databasebeta

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D4×D9×AGL(1,𝔽5) #72247359

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

Aliases

direct productD4×D9×AGL(1,𝔽5)

Splittings

FittingC5×D4×C9 ⋊ C2×C4
HallC5×C9 ⋊ C2×C4×D4
SylowC9 ⋊ C2×D4×AGL(1,𝔽5)
SylowC5 ⋊ C4×D4×D9

Subgroups

subgroupG/H
centerC2C22×D9×AGL(1,𝔽5)
commutatorC2×C5×C9C23×C4
FrattiniC2×C3C22×D3×AGL(1,𝔽5)
FittingC5×D4×C9C2×C4
socleC2×C3×C5C22×C4×D3
prime radicalD4×D5×D9C2
cosocleC2×C9×D5C24
hypercenterD4D9×AGL(1,𝔽5)
hypocenterC5×C9C2×C4×D4
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ D4

1278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9), D9×#11717375, D9×AGL(1,𝔽5)×S4
maximal normal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9)
maximal quotient ofD9×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.