Finite Group Databasebeta

C3×#17987431 #28355956

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

Aliases

direct productC3×#17987431

Splittings

FittingC33×C9×C19 ⋊ C3
SylowC19 ⋊ C3×#6893

Subgroups

subgroupG/H
centerC33C32×C19⋊C3
commutator, cosocleC32×C19C34
FrattiniC32C33×C19⋊C3
FittingC33×C9×C19C3
socleC33×C19C33
prime radicalC32×C32⋊(C19⋊C3)C3
hypercenterC33×C9C19⋊C3
hypocenterC19C3×#6893
LCSG ▷ C32×C19 ▷ C19
UCSC1 ◁ C33 ◁ C33×C9

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4617

Conjugacy classes & character table

1611 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3320);