Finite Group Databasebeta

C27×C32⋊(C43⋊C3) #44533508

order31347
automorphism?
homologyAbelianization (H1) = C32×C27 · Schur multiplier (H2) = C34

Aliases

direct productC27×C32⋊(C43⋊C3)

Splittings

FittingC32×C27×C43 ⋊ C3
SylowC43 ⋊ C27×H(3,𝔽3)

Subgroups

subgroupG/H
centerC3×C27C3×C43⋊C3
commutatorC3×C43C32×C27
FrattiniC3×C9C32×C43⋊C3
FittingC32×C27×C43C3
socleC32×C43C32×C9
prime radicalC3×C32⋊(C43⋊C3)C9
cosocleC3×C9×C43C33
hypercenterC32×C27C43⋊C3
hypocenterC43C27×H(3,𝔽3)
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C3×C27 ◁ C32×C27

292 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, 2131);