Finite Group Databasebeta

← Prev (#72244346) Next (#72244348) →

AGL(1,ℤ/9)×#509 #72244347

order3456
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/9)×#509

Splittings

Fitting3−1+2×#509 ⋊ C2
Sylow3−1+2 ⋊ C2×#509

Subgroups

subgroupG/H
centerC2C2×D8×AGL(1,ℤ/9)
commutator, cosocleC8×C9C24×C3
FrattiniC3×C8C23×C3×D3
Fitting3−1+2×#509C2
socleC2×C3C2×C3×D3×D8
hypercenter#509AGL(1,ℤ/9)
hypocenterC9C2×C3×#509
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

1245 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×AGL(1,ℤ/16)
maximal normal subgroup ofAGL(1,ℤ/9)×AGL(1,ℤ/16)

GAP

Past the SmallGroups library coverage — no SmallGroups id.