Finite Group Databasebeta

C3×#17987519 #28356576

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

Aliases

direct productC3×#17987519

Splittings

SylowC19 ⋊ C3×#6912

Subgroups

subgroupG/H
centerC32C3×C32⋊(C19⋊C3)
commutator, cosocleC32×C19C34
FrattiniC32C33×C19⋊C3
FittingC32×C19×3−1+2C3
socleC32×C19C3×H(3,𝔽3)
prime radicalC34×C19C32
hypercenterC32×3−1+2C19⋊C3
hypocenterC19C3×#6912
LCSG ▷ C32×C19 ▷ C3×C19 ▷ C19
UCSC1 ◁ C32 ◁ C34 ◁ C32×3−1+2

980 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1539

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3940);