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AGL(1,ℤ/9)×#532 #72244695

order3456
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,ℤ/9)×#532

Splittings

Fitting3−1+2×#532 ⋊ C2
Sylow3−1+2 ⋊ C2×#532

Subgroups

subgroupG/H
centerC2×C4C23×AGL(1,ℤ/9)
commutator, cosocleC22×C9C25×C3
Frattini, socleC22×C3C24×C3×D3
Fitting3−1+2×#532C2
hypercenter#532AGL(1,ℤ/9)
hypocenterC9C2×C3×#532
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ #532

5339 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#3151, AGL(1,ℤ/9)×#3184, AGL(1,ℤ/9)×#3498
maximal normal subgroup ofAGL(1,ℤ/9)×#3151, AGL(1,ℤ/9)×#3184, AGL(1,ℤ/9)×#3498
maximal quotient ofAGL(1,ℤ/9)×#3184

GAP

Past the SmallGroups library coverage — no SmallGroups id.