Finite Group Databasebeta

C9×#13095332 #28355919

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

Aliases

direct productC9×#13095332

Splittings

FittingC3×C92×C19 ⋊ C3
SylowC19 ⋊ C9×#737

Subgroups

subgroupG/H
centerC92C3×C19⋊C3
commutatorC3×C19C33×C9
FrattiniC32C33×C19⋊C3
FittingC3×C92×C19C3
socle, cosocleC32×C19C34
prime radicalC3×C32⋊(C19⋊C3)C32
hypercenterC3×C92C19⋊C3
hypocenterC19C9×#737
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C92 ◁ C3×C92

986 conjugacy classes of subgroups; only the 472 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 472 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) = 4617

Conjugacy classes & character table

1755 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3283);