Finite Group Databasebeta

C3×#17987384 #28355774

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

Aliases

direct productC3×#17987384

Splittings

SylowC19 ⋊ C3×#6882

Subgroups

subgroupG/H
centerC32#13095319
commutator, cosocleC3×C9×C19C33
FrattiniC3×C9C32×C19⋊C3
FittingC3×C19×#733C3
socleC32×C19#732
prime radicalC33×C19H(3,𝔽3)
hypercenterC3×#733C19⋊C3
hypocenterC19C3×#6882
LCSG ▷ C3×C9×C19 ▷ C32×C19 ▷ C3×C19 ▷ C19
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9 ◁ C3×#733

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1539

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, 3138);