Finite Group Databasebeta

C3×#11923956⋊C9 #44534651

order31347
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC3×#11923956⋊C9

Splittings

FittingC3×C43×C9⋊C9 ⋊ C3
SylowC43 ⋊ C3×C9×3−1+2

Subgroups

subgroupG/H
centerC33C32×C43⋊C3
commutatorC3×C43C33×C9
FrattiniC32C33×C43⋊C3
FittingC3×C43×C9⋊C9C3
socleC33×C43C33
prime radicalC33×C43⋊C3C32
cosocleC32×C43C34
hypercenterC3×C9⋊C9C43⋊C3
hypocenterC43C3×C9×3−1+2
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C33 ◁ C3×C9⋊C9

1148 conjugacy classes of subgroups; only the 508 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 508 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) = 10449

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31347, 3274);