Finite Group Databasebeta

C13⋊C3×#6910 #23748516

order9477
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC13⋊C3×#6910

Splittings

FittingC13×#6910 ⋊ C3
SylowC13 ⋊ C3×#6910

Subgroups

subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×#6910C3
socleC3×C13C32×H(3,𝔽3)
prime radicalC3×H(3,𝔽3)×C13⋊C3C3
hypercenter#6910C13⋊C3
hypocenterC13C3×#6910
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ #6910

1088 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 271 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

245 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 3925);