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C22×C5⋊AGL(1,ℤ/9) #11762009

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

Aliases

direct productC22×C5⋊AGL(1,ℤ/9)

Splittings

FittingC22×C5×3−1+2 ⋊ C2
derivedC5×C9 ⋊ C23×C3
HallC5×3−1+2 ⋊ C23
Sylow3−1+2 ⋊ C22×D5
SylowC5 ⋊ C22×AGL(1,ℤ/9)

Subgroups

subgroupG/H
center, hypercenterC22C5⋊AGL(1,ℤ/9)
commutator, cosocle, hypocenterC5×C9C23×C3
FrattiniC3C22×C3×D15
FittingC22×C5×3−1+2C2
socleC22×C3×C5C3×D3
LCSG ▷ C5×C9
UCSC1 ◁ C22

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×D5×AGL(1,ℤ/9), C22×C5⋊(C5⋊AGL(1,ℤ/9)), D4×C5⋊AGL(1,ℤ/9), …
maximal normal subgroup ofC22×D5×AGL(1,ℤ/9), D4×C5⋊AGL(1,ℤ/9), #72247428, …
maximal quotient ofC22×C5⋊(C5⋊AGL(1,ℤ/9)), D4×C5⋊AGL(1,ℤ/9), C2×D5×C5⋊AGL(1,ℤ/9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 355);