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C16×AGL(1,ℤ/9) #11720356

order864
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2

Aliases

direct productC16×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C3×C16)
unambiguous semidirect product(C16×D9)⋊C3

Splittings

FittingC16×3−1+2 ⋊ C2
derivedC9 ⋊ C2×C3×C16
Sylow3−1+2 ⋊ C2×C16

Subgroups

subgroupG/H
center, hypercenterC16AGL(1,ℤ/9)
commutator, hypocenterC9C2×C3×C16
FrattiniC3×C8C2×C3×D3
FittingC16×3−1+2C2
socleC2×C3C3×D3×C8
prime radicalC2×AGL(1,ℤ/9)C8
cosocleC8×C9C22×C3
LCSG ▷ C9
UCSC1 ◁ C16

89 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×AGL(1,ℤ/9), #10588124⋊C3, C2×C16×AGL(1,ℤ/9), …
maximal normal subgroup ofC32×AGL(1,ℤ/9), #10588124⋊C3, C2×C16×AGL(1,ℤ/9), …
maximal quotient ofC32×AGL(1,ℤ/9), #10588124⋊C3, C16×3−1+2⋊C4, …
automorphism group ofC17×D9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 323);