Finite Group Databasebeta

C3×#23782735 #44533476

order31347
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

direct productC3×#23782735

Splittings

SylowC43 ⋊ C3×#6875

Subgroups

subgroupG/H
centerC32(C43⋊C9)⋊C9
commutatorC9×C43C32×C9
FrattiniC3×C9C32×C43⋊C3
FittingC3×C43×C9⋊C9C3
socleC32×C43C9⋊C9
prime radicalC33×C433−1+2
cosocleC3×C9×C43C33
hypercenterC3×C9⋊C9C43⋊C3
hypocenterC43C3×#6875
LCSG ▷ C9×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C32×C9 ◁ C3×C9⋊C9

212 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, 2099);