Finite Group Databasebeta

← Prev (#28355936) Next (#28355938) →

C19⋊C3×C32⋊H(3,𝔽3) #28355937

order13851
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C39

Aliases

direct productC19⋊C3×C32⋊H(3,𝔽3)

Splittings

FittingC19×C32⋊H(3,𝔽3) ⋊ C3
SylowC19 ⋊ C3×C32⋊H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC32C33×C19⋊C3
commutator, socle, cosocleC32×C19C34
FittingC19×C32⋊H(3,𝔽3)C3
hypercenterC32⋊H(3,𝔽3)C19⋊C3
hypocenterC19C3×C32⋊H(3,𝔽3)
LCSG ▷ C32×C19 ▷ C19
UCSC1 ◁ C32 ◁ C32⋊H(3,𝔽3)

3824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 513

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3301);