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AGL(1,ℤ/9)×#442 #72244292

order3456
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,ℤ/9)×#442

Splittings

Fitting3−1+2×#442 ⋊ C2
Sylow3−1+2 ⋊ C2×#442

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,ℤ/9)
commutatorC4×C9C23×C3×C4
FrattiniC2×C3×C4C23×C3×D3
Fitting3−1+2×#442C2
socleC22×C3C2×C3×D3×D4
prime radicalC2×D8×AGL(1,ℤ/9)C2
cosocleC2×C4×C9C24×C3
hypercenter#442AGL(1,ℤ/9)
hypocenterC9C2×C3×#442
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #442

1890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×AGL(1,ℤ/16), AGL(1,ℤ/9)×#3184, #442×C3⋊AGL(1,ℤ/9)
maximal normal subgroup ofAGL(1,ℤ/9)×AGL(1,ℤ/16), AGL(1,ℤ/9)×#3184
maximal quotient ofAGL(1,ℤ/9)×AGL(1,ℤ/16), #442×C3⋊AGL(1,ℤ/9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.