Finite Group Databasebeta

#44534465

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

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #10624833

Subgroups

subgroupG/H
center, FrattiniC27C32×C43⋊C3
commutator, socleC3×C43C32×C27
FittingC43×#6903C3
prime radicalH(3,𝔽3)×C43C27
cosocleC27×C43C33
hypercenter#6903C43⋊C3
hypocenterC43#10624833
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C27 ◁ #6903

154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10449

Polycyclic presentation:

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

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, 3088);