Finite Group Databasebeta

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C32×#16812512 #44535284

order31347
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C37

Aliases

direct productC32×#16812512

Splittings

FittingC32×H(3,𝔽3)×C43 ⋊ C3
SylowC43 ⋊ C32×#732

Subgroups

subgroupG/H
centerC33C32⋊(C43⋊C3)
commutator, cosocleC32×C43C34
FrattiniC32C33×C43⋊C3
FittingC32×H(3,𝔽3)×C43C3
socleC33×C43H(3,𝔽3)
hypercenterC32×H(3,𝔽3)C43⋊C3
hypocenterC43C32×#732
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C33 ◁ C34 ◁ C32×H(3,𝔽3)

1376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Conjugacy classes & character table

1539 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3907);