Finite Group Databasebeta

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C4×#41×AGL(1,ℤ/9) #72268968

order3456
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#41×AGL(1,ℤ/9)

Splittings

FittingC4×#41×3−1+2 ⋊ C2
Sylow3−1+2 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC42C22×AGL(1,ℤ/9)
commutatorC2×C9C24×C3×C4
Frattini, socleC22×C3C24×C3×D3
FittingC4×#41×3−1+2C2
prime radicalC2×#41×AGL(1,ℤ/9)C2
cosocleC22×C9C25×C3
hypercenterC4×#41AGL(1,ℤ/9)
hypocenterC9C2×C3×C4×#41
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C42 ◁ C4×#41

5339 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#3498
maximal normal subgroup ofAGL(1,ℤ/9)×#3498

GAP

Past the SmallGroups library coverage — no SmallGroups id.