Finite Group Databasebeta

C32×#16812499 #44534639

order31347
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C36

Aliases

direct productC32×#16812499

Splittings

SylowC43 ⋊ C32×C9⋊C9

Subgroups

subgroupG/H
centerC34C3×C43⋊C3
commutatorC3×C43C33×C9
FrattiniC32C33×C43⋊C3
FittingC33×C9×C43C3
socle, prime radicalC34×C43C32
cosocleC32×C43C34
hypercenterC33×C9C43⋊C3
hypocenterC43C32×C9⋊C9
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C34 ◁ C33×C9

1484 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, 3262);