Finite Group Databasebeta

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#23748569

order9477
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #10624933

Subgroups

subgroupG/H
centerC3C32×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×3−1+4C3
socleC3×C13C32×H(3,𝔽3)
prime radicalC3×C13×H(3,𝔽3)C32
hypercenter3−1+4C13⋊C3
hypocenterC13#10624933
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×H(3,𝔽3) ◁ 3−1+4

936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3^6,13|a^3=f,b^3=f^2,b^a=be,e^a=ef,g^b=g^3,d^c=df

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 3978);