Finite Group Databasebeta

C3×#17987589 #28357043

order13851
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C34×C9

Aliases

direct productC3×#17987589
unambiguous semidirect product(C19⋊C3)⋊#6887

Splittings

FittingC32×C9×C19 ⋊ C9
SylowC19 ⋊ C3×#6887

Subgroups

subgroupG/H
centerC3×C9C3×#4296
commutatorC3×C19C33×C9
FrattiniC3C33×#4296
FittingC32×C9×C19C9
socleC32×C19C32×C9
prime radicalC33×C19⋊C3C32
cosocleC3×C19⋊C3C34
hypercenterC32×C9#4296
hypocenterC19C3×#6887
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C3×C9 ◁ C32×C9

1052 conjugacy classes of subgroups; only the 450 normal subgroups are shown.

normal subgroups only

This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 450 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) = 1539

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, 4407);