Finite Group Databasebeta

C19⋊C3×#6913 #28356577

order13851
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC19⋊C3×#6913

Splittings

FittingC19×#6913 ⋊ C3
SylowC19 ⋊ C3×#6913

Subgroups

subgroupG/H
centerC3C3×H(3,𝔽3)×C19⋊C3
commutator, cosocleC32×C19C34
FrattiniC32C33×C19⋊C3
FittingC19×#6913C3
socleC3×C19C32×H(3,𝔽3)
hypercenter#6913C19⋊C3
hypocenterC19C3×#6913
LCSG ▷ C32×C19 ▷ C3×C19 ▷ C19
UCSC1 ◁ C3 ◁ C3×C9 ◁ #6913

992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 513

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3941);