Finite Group Databasebeta

C3×#23782806 #44534695

order31347
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC3×#23782806

Splittings

SylowC43 ⋊ C3×#6893

Subgroups

subgroupG/H
centerC33C32×C43⋊C3
commutator, cosocleC32×C43C34
FrattiniC32C33×C43⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C43C3
socleC33×C43C33
hypercenterC32×H(3,𝔽3)C43⋊C3
hypocenterC43C3×#6893
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Conjugacy classes & character table

1539 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3318);