Finite Group Databasebeta

← Prev (#72247395) Next (#72247397) →

C22×AGL(1,ℤ/9)×#1043 #72247396

order21600
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×AGL(1,ℤ/9)×#1043

Splittings

FittingC22×C52×3−1+2 ⋊ C2×C4
derivedC52×C9 ⋊ C23×C3×C4
HallC52×3−1+2 ⋊ C23×C4
Sylow3−1+2 ⋊ C23×#1043
SylowC52 ⋊ C22×C4×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC22AGL(1,ℤ/9)×#1043
commutator, hypocenterC52×C9C23×C3×C4
FrattiniC3C22×C3×D3×#1043
FittingC22×C52×3−1+2C2×C4
socleC22×C3×C52C3×C4×D3
prime radicalC22×C5⋊D5×AGL(1,ℤ/9)C2
cosocleC9×C5⋊D5C24×C3
LCSG ▷ C52×C9
UCSC1 ◁ C22

5880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 900

Conjugacy classes & character table

400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#11717375
maximal normal subgroup ofAGL(1,ℤ/9)×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.