Finite Group Databasebeta

C3×#11760453 #15691692

order3159
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC3×#11760453

Splittings

FittingC32×C9×C13 ⋊ C3
SylowC13 ⋊ C3×#737

Subgroups

subgroupG/H
centerC3×C9C3×C13⋊C3
commutator, cosocleC3×C13C34
FrattiniC3C33×C13⋊C3
FittingC32×C9×C13C3
socleC32×C13C33
prime radicalC3×C32⋊(C13⋊C3)C3
hypercenterC32×C9C13⋊C3
hypocenterC13C3×#737
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C3×C9 ◁ C32×C9

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1053

Conjugacy classes & character table

423 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 302);