Finite Group Databasebeta

← Prev (#23748556) Next (#23748558) →

#23748557

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

Aliases

No aliases for this group.

Splittings

FittingC32×C13×H(3,𝔽3) ⋊ C3
SylowC13 ⋊ #10624930

Subgroups

subgroupG/H
centerC3C32×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC32×C13×H(3,𝔽3)C3
socleC3×C13C32×H(3,𝔽3)
hypercenterC32×H(3,𝔽3)C13⋊C3
hypocenterC13#10624930
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×H(3,𝔽3) ◁ C32×H(3,𝔽3)

1118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

501 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 3966);