Finite Group Databasebeta

C13⋊C3×#737 #15691690

order3159
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC13⋊C3×#737

Splittings

FittingC13×#737 ⋊ C3
SylowC13 ⋊ C3×#737

Subgroups

subgroupG/H
centerC9C32×C13⋊C3
commutator, socle, cosocleC3×C13C34
FrattiniC3C33×C13⋊C3
FittingC13×#737C3
prime radicalH(3,𝔽3)×C13⋊C3C3
hypercenter#737C13⋊C3
hypocenterC13C3×#737
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C9 ◁ #737

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 351

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 300);