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AGL(1,ℤ/9)×#535 #72244457

order3456
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,ℤ/9)×#535

Splittings

Fitting3−1+2×#535 ⋊ C2
Sylow3−1+2 ⋊ C2×#535

Subgroups

subgroupG/H
centerC22C24×AGL(1,ℤ/9)
commutator, cosocleC22×C9C25×C3
Frattini, socleC22×C3C24×C3×D3
Fitting3−1+2×#535C2
hypercenter#535AGL(1,ℤ/9)
hypocenterC9C2×C3×#535
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #535

5855 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#3484, AGL(1,ℤ/9)×#3498
maximal normal subgroup ofAGL(1,ℤ/9)×#3484, AGL(1,ℤ/9)×#3498

GAP

Past the SmallGroups library coverage — no SmallGroups id.