Finite Group Databasebeta

C32×#16812524 #44535397

order31347
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC32×#16812524

Splittings

SylowC43 ⋊ C32×#737

Subgroups

subgroupG/H
centerC33C32×C43⋊C3
commutator, cosocleC3×C43C35
FrattiniC3C34×C43⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C43C3
socleC33×C43C33
hypercenterC32×H(3,𝔽3)C43⋊C3
hypocenterC43C32×#737
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

5804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 4020);