Finite Group Databasebeta

C3×#17987547 #28356665

order13851
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC3×#17987547

Splittings

SylowC19 ⋊ C3×3−1+4

Subgroups

subgroupG/H
centerC32C33×C19⋊C3
commutator, cosocleC3×C19C35
FrattiniC3C34×C19⋊C3
Fitting, prime radicalC32×C19×H(3,𝔽3)C3
socleC32×C19C34
hypercenterC32×H(3,𝔽3)C19⋊C3
hypocenterC19C3×3−1+4
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C32 ◁ C32×H(3,𝔽3)

5588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1539

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4029);