Finite Group Databasebeta

C3×#17987598 #28357057

order13851
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC3×#17987598

Splittings

SylowC19 ⋊ C3×#6903

Subgroups

subgroupG/H
centerC32C32×#4296
commutatorC3×C19C33×C9
FrattiniC3C33×#4296
Fitting, prime radicalC3×C19×H(3,𝔽3)C9
socleC32×C19C32×C9
cosocle#4294C34
hypercenterC3×H(3,𝔽3)#4296
hypocenterC19C3×#6903
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4421);