Finite Group Databasebeta

D3×C9⋊(C22⋊C9) #14518176

order1944
automorphism?
homologyAbelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C3

Aliases

direct productD3×C9⋊(C22⋊C9)
unambiguous semidirect productC3⋊(C2×C9⋊(C22⋊C9))
unambiguous semidirect product(D3×C9)⋊(C22⋊C9)

Subgroups

subgroupG/H
center, FrattiniC32C3×D3×A4
commutatorC22×C32C2×C3×C9
FittingC22×C32×C9C2×C3
socle, cosocleC22×C33C2×C32
prime radicalC22×C32×D3C32
hypercenterC3×C9D3×A4
hypocenterC22×C3C2×C9⋊C9
LCSG ▷ C22×C32 ▷ C22×C3
UCSC1 ◁ C32 ◁ C3×C9

287 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 324

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2570);