Finite Group Databasebeta

← Prev (#46799001) Next (#46799003) →

C3×C13⋊C3×C289 #46799002

order33813
automorphism?
homologyAbelianization (H1) = C32×C289 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13⋊C3×C289
unambiguous semidirect productC13⋊(C32×C289)
unambiguous semidirect product(C3×C13)⋊(C3×C289)
unambiguous semidirect product(C13×C289)⋊C32
unambiguous semidirect product(C3×C13×C289)⋊C3

Splittings

FittingC3×C13×C289 ⋊ C3
derived, SylowC13 ⋊ C32×C289
HallC13×C289 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C289C13⋊C3
commutator, hypocenterC13C32×C289
FrattiniC17C3×C17×C13⋊C3
FittingC3×C13×C289C3
socleC3×C13×C17C3×C17
prime radicalC3×C17×C13⋊C3C17
cosocleC13×C17C32×C17
LCSG ▷ C13
UCSC1 ◁ C3×C289

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11271

Conjugacy classes & character table

6069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33813, 4);