Finite Group Databasebeta

#44532234

order31347
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C3×C92

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #10624544

Subgroups

subgroupG/H
center, FrattiniC33C32×C43⋊C3
commutatorC3×C43C3×C92
FittingC43×#6855C3
socle, prime radical, cosocleC33×C43C33
hypercenter#6855C43⋊C3
hypocenterC43#10624544
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C33 ◁ #6855

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31347

Polycyclic presentation:

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

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, 857);