Finite Group Databasebeta

← Prev (#72247469) Next (#72247471) →

D4×AGL(1,𝔽5)×AGL(1,ℤ/9) #72247470

order8640
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×AGL(1,𝔽5)×AGL(1,ℤ/9)

Splittings

FittingC5×D4×3−1+2 ⋊ C2×C4
HallC5×3−1+2 ⋊ C2×C4×D4
Sylow3−1+2 ⋊ C2×D4×AGL(1,𝔽5)
SylowC5 ⋊ C4×D4×AGL(1,ℤ/9)

Subgroups

subgroupG/H
centerC2C22×AGL(1,𝔽5)×AGL(1,ℤ/9)
commutatorC2×C5×C9C23×C3×C4
FrattiniC2×C3C22×C3×D3×AGL(1,𝔽5)
FittingC5×D4×3−1+2C2×C4
socleC2×C3×C5C22×C3×C4×D3
prime radicalD4×D5×AGL(1,ℤ/9)C2
cosocleC2×C9×D5C24×C3
hypercenterD4AGL(1,𝔽5)×AGL(1,ℤ/9)
hypocenterC5×C9C2×C3×C4×D4
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C2 ◁ D4

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#11717375, AGL(1,𝔽5)×S4×AGL(1,ℤ/9)
maximal quotient ofAGL(1,ℤ/9)×#11717375
holomorph ofC4×C5×C9

GAP

Past the SmallGroups library coverage — no SmallGroups id.