Finite Group Databasebeta

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C2×C5×D9⋊C9 #13108272

order1620
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D9⋊C9
unambiguous semidirect productD9⋊(C2×C5×C9)
unambiguous semidirect product(C2×D9)⋊(C5×C9)
unambiguous semidirect product(C9⋊C9)⋊(C22×C5)
unambiguous semidirect product(C2×C9⋊C9)⋊(C2×C5)
unambiguous semidirect product(C2×C5×D9)⋊C9

Splittings

FittingC2×C5×C9⋊C9 ⋊ C2
derivedC9 ⋊ C22×C5×C9
HallC5×C9⋊C9 ⋊ C22
SylowC9⋊C9 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5AGL(1,ℤ/9)
commutator, hypocenterC9C22×C5×C9
FrattiniC32C2×C3×C5×D3
FittingC2×C5×C9⋊C9C2
socleC2×C32×C5C3×D3
prime radicalC2×C3×C5×D9C3
cosocleC3×C9C22×C3×C5
LCSG ▷ C9
UCSC1 ◁ C2×C3×C5

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 178);