Finite Group Databasebeta

C32⋊C9×C43⋊C9 #44532239

order31347
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C33×C9

Aliases

direct productC32⋊C9×C43⋊C9

Splittings

SylowC43 ⋊ C9×C32⋊C9

Subgroups

subgroupG/H
center, FrattiniC33C32×C43⋊C3
commutatorC3×C43C3×C92
FittingC3×C43×C32⋊C9C3
socle, cosocleC33×C43C33
prime radicalC34×C43C32
hypercenterC3×C32⋊C9C43⋊C3
hypocenterC43C9×C32⋊C9
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C33 ◁ C3×C32⋊C9

662 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 238 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, 862);