Finite Group Databasebeta

← Prev (#72247366) Next (#72247368) →

C4×AGL(1,𝔽5)×AGL(1,ℤ/9) #72247367

order4320
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×AGL(1,𝔽5)×AGL(1,ℤ/9)

Splittings

FittingC4×C5×3−1+2 ⋊ C2×C4
derivedC5×C9 ⋊ C2×C3×C42
HallC5×3−1+2 ⋊ C2×C42
Sylow3−1+2 ⋊ C2×C4×AGL(1,𝔽5)
SylowC5 ⋊ C42×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC4AGL(1,𝔽5)×AGL(1,ℤ/9)
commutator, hypocenterC5×C9C2×C3×C42
FrattiniC2×C3C2×C3×D3×AGL(1,𝔽5)
FittingC4×C5×3−1+2C2×C4
socleC2×C3×C5C2×C3×C4×D3
prime radicalC2×D5×AGL(1,ℤ/9)C22
cosocleC2×C9×D5C23×C3
LCSG ▷ C5×C9
UCSC1 ◁ C4

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)2×AGL(1,ℤ/9), D4×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,ℤ/9)×#87830
maximal normal subgroup ofD4×AGL(1,𝔽5)×AGL(1,ℤ/9)
maximal quotient ofAGL(1,𝔽5)2×AGL(1,ℤ/9), AGL(1,ℤ/9)×#87830

GAP

Past the SmallGroups library coverage — no SmallGroups id.