Finite Group Databasebeta

#44532254

order31347
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #10624549

Subgroups

subgroupG/H
center, FrattiniC33C32×C43⋊C3
commutatorC32×C43C32×C9
FittingC33×C9×C43C3
socle, cosocleC33×C43C33
prime radicalC34×C43C32
hypercenterC33×C9C43⋊C3
hypocenterC43#10624549
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C33 ◁ C33×C9

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Polycyclic presentation:

3^6,43|a^3=f,c^3=d,b^a=bd,c^a=ce,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, 877);