Finite Group Databasebeta

C9×#16812504 #44533345

order31347
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C3×C9

Aliases

direct productC9×#16812504

Splittings

FittingC9×C27×C43 ⋊ C3
SylowC43 ⋊ C9×C27⋊C3

Subgroups

subgroupG/H
centerC92C3×C43⋊C3
commutatorC3×C43C3×C92
FrattiniC3×C9C32×C43⋊C3
FittingC9×C27×C43C3
socleC32×C43C32×C9
prime radicalC32×C43⋊C3C3×C9
cosocleC3×C9×C43C33
hypercenterC9×C27C43⋊C3
hypocenterC43C9×C27⋊C3
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C92 ◁ C9×C27

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

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, 1968);