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C2×D3×AGL(1,ℤ/9) #10620085

order648
isoclinismisoclinic class of D3×AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productC2×D3×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C2×C3×D3)
unambiguous semidirect product(D3×D9)⋊(C2×C3)
unambiguous semidirect product(C3×AGL(1,ℤ/9))⋊C22
unambiguous semidirect product(D3×3−1+2)⋊C22
unambiguous semidirect product(C3⋊AGL(1,ℤ/9))⋊C22
unambiguous semidirect product(C2×D3×D9)⋊C3

Splittings

FittingC2×C3×3−1+2 ⋊ C22
derivedC3×C9 ⋊ C23×C3
SylowC3×3−1+2 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC2D3×AGL(1,ℤ/9)
commutator, cosocle, hypocenterC3×C9C23×C3
FrattiniC3C2×C3×D32
FittingC2×C3×3−1+2C22
socleC2×C32C2×C3×D3
LCSG ▷ C3×C9
UCSC1 ◁ C2

241 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 241 conjugacy classes of subgroups — too many to draw. Only its 63 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) = 36

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D3×AGL(1,ℤ/9), D12×AGL(1,ℤ/9), D3×C4⋊AGL(1,ℤ/9), …
maximal normal subgroup ofC4×D3×AGL(1,ℤ/9), D12×AGL(1,ℤ/9), D3×C4⋊AGL(1,ℤ/9), …
maximal quotient ofDic6×AGL(1,ℤ/9), #88641⋊C3, #88634⋊C3, …
automorphism group ofC3×3−1+2⋊C4, C3×D3×D9, C2×C3×AGL(1,ℤ/9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 604);