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C3×C4×AGL(1,ℤ/9) #10619934

order648
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C4×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C32×C4)
unambiguous semidirect product(C4×D9)⋊C32
unambiguous semidirect product(C3×C4×D9)⋊C3

Splittings

FittingC3×C4×3−1+2 ⋊ C2
derivedC9 ⋊ C2×C32×C4
SylowC3×3−1+2 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC3×C4AGL(1,ℤ/9)
commutator, hypocenterC9C2×C32×C4
FrattiniC2×C3C2×C32×D3
FittingC3×C4×3−1+2C2
socleC2×C32C2×C3×D3
prime radicalC2×C3×AGL(1,ℤ/9)C2
cosocleC2×C9C22×C32
LCSG ▷ C9
UCSC1 ◁ C3×C4

174 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 72

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊C8×AGL(1,ℤ/9), #88413⋊C3, C3×C8×AGL(1,ℤ/9), …
maximal normal subgroup ofC3⋊C8×AGL(1,ℤ/9), #88413⋊C3, C3×C8×AGL(1,ℤ/9), …
maximal quotient ofC3×C8×AGL(1,ℤ/9), C3×#3663⋊C3, C3×C4×3−1+2⋊C4, …
automorphism group ofC13×D9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 453);