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AGL(1,ℤ/9)×#492 #72244663

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

Aliases

direct productAGL(1,ℤ/9)×#492

Splittings

Fitting3−1+2×#492 ⋊ C2
Sylow3−1+2 ⋊ C2×#492

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,ℤ/9)
commutator, cosocleC2×C4×C9C24×C3
FrattiniC2×C3×C4C23×C3×D3
Fitting3−1+2×#492C2
socleC22×C3C2×C3×D3×D4
prime radical#127×AGL(1,ℤ/9)C2
hypercenter#492AGL(1,ℤ/9)
hypocenterC9C2×C3×#492
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #492

2039 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)×#3151, AGL(1,ℤ/9)×#1715, AGL(1,ℤ/9)×#1721, …
maximal normal subgroup ofAGL(1,ℤ/9)×#3151, AGL(1,ℤ/9)×#1715, AGL(1,ℤ/9)×#1721, …
maximal quotient ofAGL(1,ℤ/9)×#1715, AGL(1,ℤ/9)×#1705

GAP

Past the SmallGroups library coverage — no SmallGroups id.