Finite Group Databasebeta

C3×#23782746 #44534469

order31347
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#23782746

Splittings

FittingC3×C92×C43 ⋊ C3
SylowC43 ⋊ C3×#6878

Subgroups

subgroupG/H
centerC32#16812513
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC3×C92×C43C3
socleC32×C43#732
prime radicalC3×#16812513C3
hypercenterC3×C92C43⋊C3
hypocenterC43C3×#6878
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9 ◁ C3×C92

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3483

Conjugacy classes & character table

3507 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3092);