Finite Group Databasebeta

C3×#24924308 #44565448

order32157
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#24924308

Splittings

SylowC397 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C397⋊C3
commutator, cosocleC3×C397C33
FrattiniC3C32×C397⋊C3
Fitting, prime radicalC33×C397C3
socleC32×C397C32
hypercenterC33C397⋊C3
hypocenterC397C3×3−1+2
LCSG ▷ C3×C397 ▷ C397
UCSC1 ◁ C32 ◁ C33

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10719

Conjugacy classes & character table

3597 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32157, 45);