Finite Group Databasebeta

C32×#66849 #15691687

order3159
isoclinismisoclinic class of #66848
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC32×#66849

Splittings

FittingC32×C9×C13 ⋊ C3
SylowC13 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC33C3×C13⋊C3
commutator, cosocleC3×C13C34
FrattiniC3C33×C13⋊C3
FittingC32×C9×C13C3
socleC33×C13C32
prime radicalC33×C13⋊C3C3
hypercenterC32×C9C13⋊C3
hypocenterC13C32×3−1+2
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C33 ◁ C32×C9

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1053

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 297);