Finite Group Databasebeta

C3×#11760441 #15691643

order3159
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

direct productC3×#11760441

Splittings

FittingC32×C9×C13 ⋊ C3
SylowC13 ⋊ C3×#732

Subgroups

subgroupG/H
centerC32C32⋊(C13⋊C3)
commutator, cosocleC32×C13C33
FrattiniC32C32×C13⋊C3
FittingC32×C9×C13C3
socleC32×C13H(3,𝔽3)
hypercenterC32×C9C13⋊C3
hypocenterC13C3×#732
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1053

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 253);