Finite Group Databasebeta

C3×C19⋊H(5,𝔽3) #28356660

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

Aliases

direct productC3×C19⋊H(5,𝔽3)
unambiguous semidirect product(C3×C19)⋊H(5,𝔽3)

Splittings

FittingC32×C19×H(3,𝔽3) ⋊ C3
SylowC19 ⋊ C3×H(5,𝔽3)

Subgroups

subgroupG/H
centerC32C33×C19⋊C3
commutator, cosocleC3×C19C35
FrattiniC3C34×C19⋊C3
FittingC32×C19×H(3,𝔽3)C3
socleC32×C19C34
hypercenterC32×H(3,𝔽3)C19⋊C3
hypocenterC19C3×H(5,𝔽3)
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C32 ◁ C32×H(3,𝔽3)

6776 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, 4024);