Finite Group Databasebeta

#44533361

order31347
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #10624683

Subgroups

subgroupG/H
center, FrattiniC3×C9C32×C43⋊C3
commutator, socleC32×C43C32×C9
FittingC33×C9×C43C3
prime radicalC34×C43C9
cosocleC3×C9×C43C33
hypercenterC33×C9C43⋊C3
hypocenterC43#10624683
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C3×C9 ◁ C33×C9

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3483

Polycyclic presentation:

3^6,43|a^3=e,e^3=f,b^a=bd,c^a=cf,g^a=g^36

Conjugacy classes & character table

3555 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 1984);