Finite Group Databasebeta

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AGL(1,ℤ/9)×C3⋊D9 #72243288

order2916
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3

Aliases

direct productAGL(1,ℤ/9)×C3⋊D9

Splittings

Fitting, SylowC3×C9×3−1+2 ⋊ C22
derivedC3×C92 ⋊ C22×C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C92C22×C3
FrattiniC32C3×D3×C3⋊D3
FittingC3×C9×3−1+2C22
socleC33C3×D32
LCSG ▷ C3×C92
UCSC1

610 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/9)×C9⋊D9, AGL(1,ℤ/9)×C3⋊AGL(1,ℤ/9), #72243349, …
maximal normal subgroup ofAGL(1,ℤ/9)×C3⋊AGL(1,ℤ/9), D3×D9×AGL(1,ℤ/9)
maximal quotient ofAGL(1,ℤ/9)×C9⋊D9, #72243349, #72254062

GAP

Past the SmallGroups library coverage — no SmallGroups id.