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C22×C3×AGL(1,ℤ/9) #10620107

order648
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3

Aliases

direct productC22×C3×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C22×C32)

Splittings

FittingC22×C3×3−1+2 ⋊ C2
derivedC9 ⋊ C23×C32
SylowC3×3−1+2 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22×C3AGL(1,ℤ/9)
commutator, cosocle, hypocenterC9C23×C32
FrattiniC3C22×C32×D3
FittingC22×C3×3−1+2C2
socleC22×C32C3×D3
LCSG ▷ C9
UCSC1 ◁ C22×C3

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,ℤ/9))⋊Dic3, C3×(C2×AGL(1,ℤ/9))⋊C4, C2×Dic3×AGL(1,ℤ/9), …
maximal normal subgroup of(C2×AGL(1,ℤ/9))⋊Dic3, C3×(C2×AGL(1,ℤ/9))⋊C4, C2×Dic3×AGL(1,ℤ/9), …
maximal quotient ofC2×C3×3−1+2⋊Q8, C2×C3×C4×AGL(1,ℤ/9), C2×C3×C4⋊AGL(1,ℤ/9), …
automorphism group ofC7×Dic9, C2×C7×D9, C9×Dic9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 626);