Finite Group Databasebeta

C3×C13⋊C3×#737 #23748610

order9477
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC3×C13⋊C3×#737

Splittings

FittingC3×C13×#737 ⋊ C3
SylowC13 ⋊ C32×#737

Subgroups

subgroupG/H
centerC3×C9C32×C13⋊C3
commutator, cosocleC3×C13C35
FrattiniC3C34×C13⋊C3
FittingC3×C13×#737C3
socleC32×C13C34
prime radicalC3×H(3,𝔽3)×C13⋊C3C3
hypercenterC3×#737C13⋊C3
hypocenterC13C32×#737
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C3×C9 ◁ C3×#737

5804 conjugacy classes of subgroups; only the 2902 normal subgroups are shown.

normal subgroups only

This group has 5804 conjugacy classes of subgroups — too many to draw. Only its 2902 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

693 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4019);