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C22×C5×AGL(1,ℤ/9) #11762005

order1080
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23

Aliases

direct productC22×C5×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C22×C3×C5)
unambiguous semidirect product3−1+2⋊(C23×C5)
unambiguous semidirect product(C2×3−1+2)⋊(C22×C5)

Splittings

FittingC22×C5×3−1+2 ⋊ C2
derivedC9 ⋊ C23×C3×C5
HallC5×3−1+2 ⋊ C23
Sylow3−1+2 ⋊ C23×C5

Subgroups

subgroupG/H
center, hypercenterC22×C5AGL(1,ℤ/9)
commutator, cosocle, hypocenterC9C23×C3×C5
FrattiniC3C22×C3×C5×D3
FittingC22×C5×3−1+2C2
socleC22×C3×C5C3×D3
LCSG ▷ C9
UCSC1 ◁ C22×C5

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×D5×AGL(1,ℤ/9), C22×C52×AGL(1,ℤ/9), C5×D4×AGL(1,ℤ/9), …
maximal normal subgroup ofC22×D5×AGL(1,ℤ/9), C22×C52×AGL(1,ℤ/9), C5×D4×AGL(1,ℤ/9), …
maximal quotient ofC22×C52×AGL(1,ℤ/9), C5×D4×AGL(1,ℤ/9), C2×C5×D5×AGL(1,ℤ/9), …
automorphism group ofC11×Dic9, C2×C11×D9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 351);