Finite Group Databasebeta

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AGL(1,ℤ/9)×#453 #72220086

order3456
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,ℤ/9)×#453

Splittings

Fitting3−1+2×#453 ⋊ C2
Sylow3−1+2 ⋊ C2×#453

Subgroups

subgroupG/H
centerC2#120×AGL(1,ℤ/9)
commutator, cosocleC2×C4×C9C24×C3
FrattiniC2×C3×C4C23×C3×D3
Fitting3−1+2×#453C2
socleC2×C3C3×D3×#120
hypercenter#453AGL(1,ℤ/9)
hypocenterC9C2×C3×#453
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

2616 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72220090, AGL(1,ℤ/9)×#5935, C2×AGL(1,ℤ/9)×#453
maximal normal subgroup ofC2×AGL(1,ℤ/9)×#453
maximal quotient of#72220090, C2×AGL(1,ℤ/9)×#453
holomorph ofD4×C9

GAP

Past the SmallGroups library coverage — no SmallGroups id.