Finite Group Databasebeta

#23748597

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

Aliases

No aliases for this group.

Splittings

FittingC13×#6913 ⋊ C3
SylowC13 ⋊ #10624936

Subgroups

subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×#6913C3
socleC3×C13C32×H(3,𝔽3)
hypercenter#6913C13⋊C3
hypocenterC13#10624936
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×C9 ◁ #6913

948 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3^6,13|b^3=f^2,c^3=f,b^a=be,e^a=ef,g^b=g^9,d^c=df,g^d=g^3

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4006);