Finite Group Databasebeta

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C4⋊(C3⋊(C3⋊(C3⋊D9))) #14519009

order1944
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C36

Aliases

unambiguous semidirect productC4⋊(C3⋊(C3⋊(C3⋊D9)))

Splittings

FittingC33×C4×C9 ⋊ C2
SylowC33×C9 ⋊ D4

Subgroups

subgroupG/H
centerC2C2×C3⋊(C3⋊(C3⋊D9))
commutator, cosocleC2×C33×C9C22
FrattiniC2×C3C2×C3⋊(C3⋊(C3⋊D3))
FittingC33×C4×C9C2
socleC2×C34C2×D3
hypercenterC4C3⋊(C3⋊(C3⋊D9))
hypocenterC33×C9D4
LCSG ▷ C2×C33×C9 ▷ C33×C9
UCSC1 ◁ C2 ◁ C4

3168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 972

Polycyclic presentation:

2^3,3^5|b^2=c,g^3=h,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^2h^2,h^a=h^2

Conjugacy classes & character table

489 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3403);