Finite Group Databasebeta

C3×C9×#638 #14518949

order1944
isoclinismisoclinic class of #634
automorphism?
homologyAbelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C32

Aliases

direct productC3×C9×#638

Splittings

FittingC22×C33×C9 ⋊ C2
SylowC33×C9 ⋊ D4

Subgroups

subgroupG/H
centerC2×C3×C9C2×C3⋊D3
commutatorC2×C32C22×C3×C9
FrattiniC2×C3C2×C32×C3⋊D3
FittingC22×C33×C9C2
socleC2×C34C22×C3
prime radicalC32×#638C3
cosocleC2×C33C22×C32
hypercenterC22×C3×C9C3⋊D3
hypocenterC32C3×D4×C9
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C9 ◁ C22×C3×C9

1320 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 210 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) = 108

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3343);