Finite Group Databasebeta

← Prev (#28357044) Next (#28357046) →

C3×3−1+2×#4296 #28357045

order13851
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC3×3−1+2×#4296
unambiguous semidirect product(C19⋊C3)⋊(C9×3−1+2)

Splittings

FittingC3×C19×3−1+2 ⋊ C9
SylowC19 ⋊ C3×C9×3−1+2

Subgroups

subgroupG/H
centerC32C32×#4296
commutatorC3×C19C33×C9
FrattiniC3C33×#4296
FittingC3×C19×3−1+2C9
socleC32×C19C32×C9
prime radicalC33×C19⋊C3C32
cosocleC3×C19⋊C3C34
hypercenterC3×3−1+2#4296
hypocenterC19C3×C9×3−1+2
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C32 ◁ C3×3−1+2

1148 conjugacy classes of subgroups; only the 468 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 468 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 513

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4409);