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C2×C5×AGL(1,ℤ/9) #10587408

order540
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×AGL(1,ℤ/9)
unambiguous semidirect productD9⋊(C2×C3×C5)
unambiguous semidirect product3−1+2⋊(C22×C5)
unambiguous semidirect product(C2×D9)⋊(C3×C5)
unambiguous semidirect product(C2×3−1+2)⋊(C2×C5)
unambiguous semidirect product(C2×C5×D9)⋊C3

Splittings

FittingC2×C5×3−1+2 ⋊ C2
derivedC9 ⋊ C22×C3×C5
HallC5×3−1+2 ⋊ C22
Sylow3−1+2 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5AGL(1,ℤ/9)
commutator, cosocle, hypocenterC9C22×C3×C5
FrattiniC3C2×C3×C5×D3
FittingC2×C5×3−1+2C2
socleC2×C3×C5C3×D3
LCSG ▷ C9
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×AGL(1,ℤ/9), #67080⋊C3, #67082⋊C3, …
maximal normal subgroup ofDic5×AGL(1,ℤ/9), #67080⋊C3, #67082⋊C3, …
maximal quotient ofC5×3−1+2⋊Q8, C4×C5×AGL(1,ℤ/9), C5×C4⋊AGL(1,ℤ/9), …
automorphism group ofC11×D9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 68);