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D32×AGL(1,ℤ/9) #14519172

order1944
isoclinismisoclinic class of D32×AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productD32×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C3×D32)
unambiguous semidirect product(D3×D9)⋊(C3×D3)
unambiguous semidirect product(D32×D9)⋊C3
unambiguous semidirect product(C3×D3×AGL(1,ℤ/9))⋊C2
unambiguous semidirect product(C3⋊D3×AGL(1,ℤ/9))⋊C2
unambiguous semidirect product(D3×C3⋊AGL(1,ℤ/9))⋊C2

Splittings

Fitting, SylowC32×3−1+2 ⋊ C23
derivedC32×C9 ⋊ C23×C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C9C23×C3
FrattiniC3C3×D33
FittingC32×3−1+2C23
socleC33C22×C3×D3
LCSG ▷ C32×C9
UCSC1

638 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 86 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

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#92265⋊C2, C2×D32×AGL(1,ℤ/9), D3×D9×AGL(1,ℤ/9), …
maximal normal subgroup ofC2×D32×AGL(1,ℤ/9), C3×D32×AGL(1,ℤ/9)
maximal quotient ofD3×#92265⋊C2, C2×D32×AGL(1,ℤ/9), AGL(1,ℤ/9)×#626, …
holomorph ofD3×C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3566);