Finite Group Databasebeta

C3×#23782707 #44533342

order31347
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C33

Aliases

direct productC3×#23782707

Splittings

SylowC43 ⋊ C3×#6864

Subgroups

subgroupG/H
centerC32×C9C3×C43⋊C3
commutatorC3×C43C3×C92
FrattiniC3×C9C32×C43⋊C3
FittingC32×C27×C43C3
socle, prime radicalC33×C43C3×C9
cosocleC3×C9×C43C33
hypercenterC32×C27C43⋊C3
hypocenterC43C3×#6864
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C32×C9 ◁ C32×C27

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31347

Conjugacy classes & character table

3699 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 1965);