Finite Group Databasebeta

C3×#17987330 #28354601

order13851
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C33

Aliases

direct productC3×#17987330

Splittings

SylowC19 ⋊ C3×#6864

Subgroups

subgroupG/H
centerC32×C9C3×C19⋊C3
commutatorC3×C19C3×C92
FrattiniC3×C9C32×C19⋊C3
FittingC32×C19×C27C3
socle, prime radicalC33×C19C3×C9
cosocleC3×C9×C19C33
hypercenterC32×C27C19⋊C3
hypocenterC19C3×#6864
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C32×C9 ◁ C32×C27

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13851

Conjugacy classes & character table

1755 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 1965);