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AGL(1,ℤ/9)×#360 #72244354

order3456
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productAGL(1,ℤ/9)×#360

Splittings

Fitting3−1+2×#360 ⋊ C2
Sylow3−1+2 ⋊ C2×#360

Subgroups

subgroupG/H
centerC2#102×AGL(1,ℤ/9)
commutatorC8×C9C22×C3×C4
FrattiniC2×C3×C8C22×C3×D3
Fitting3−1+2×#360C2
socleC2×C3C3×D3×#102
prime radical#135×AGL(1,ℤ/9)C2
cosocleC2×C8×C9C23×C3
hypercenter#360AGL(1,ℤ/9)
hypocenterC9C2×C3×#360
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

725 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.