Finite Group Databasebeta

C3×#23782896 #44535317

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

Aliases

direct productC3×#23782896

Splittings

SylowC43 ⋊ C3×#6912

Subgroups

subgroupG/H
centerC32C3×C32⋊(C43⋊C3)
commutator, cosocleC32×C43C34
FrattiniC32C33×C43⋊C3
FittingC32×3−1+2×C43C3
socleC32×C43C3×H(3,𝔽3)
prime radicalC34×C43C32
hypercenterC32×3−1+2C43⋊C3
hypocenterC43C3×#6912
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C34 ◁ C32×3−1+2

980 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3483

Conjugacy classes & character table

1491 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3940);