Finite Group Databasebeta

#23748641

order9477
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

FittingC33×C9 ⋊ C13⋊C3

Subgroups

subgroupG/H
center, FrattiniC3C3×(C33⋊C13)⋊C3
commutator, cosocleC3×C33⋊C13C32
FittingC33×C9C13⋊C3
socleC34C3×C13⋊C3
prime radicalC3×(C33⋊C13)⋊C3C3
hypercenterC9(C33⋊C13)⋊C3
hypocenterC33⋊C133−1+2
LCSG ▷ C3×C33⋊C13 ▷ C33⋊C13
UCSC1 ◁ C3 ◁ C9

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3,13,3^5|c^3=g^2,b^a=b^9,c^a=cg,d^a=de^2f,e^a=ef,d^b=d^2e^2f,e^b=d^2e^2,f^b=e^2f^2

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4050);