Finite Group Databasebeta

← Prev (#44534677) Next (#44534679) →

C43⋊C3×C32⋊H(3,𝔽3) #44534678

order31347
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C39

Aliases

direct productC43⋊C3×C32⋊H(3,𝔽3)

Splittings

FittingC43×C32⋊H(3,𝔽3) ⋊ C3
SylowC43 ⋊ C3×C32⋊H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC43×C32⋊H(3,𝔽3)C3
hypercenterC32⋊H(3,𝔽3)C43⋊C3
hypocenterC43C3×C32⋊H(3,𝔽3)
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ C32⋊H(3,𝔽3)

3824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1161

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3301);