Finite Group Databasebeta

C2×Dic3×C9⋊C9 #14517411

order1944
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C9 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×Dic3×C9⋊C9
unambiguous semidirect product(C2×C3)⋊(C4×C9⋊C9)
unambiguous semidirect product(C2×C9×Dic3)⋊C9

Splittings

SylowC3×C9⋊C9 ⋊ C2×C4

Subgroups

subgroupG/H
centerC22×C32C32×D3
commutatorC32C2×C3×C4×C9
FrattiniC2×C32C2×C32×D3
FittingC22×C3×C9⋊C9C2
socle, prime radicalC22×C33C2×C32
cosocleC2×C33C22×C32
hypercenterC22×C9⋊C9D3
hypocenterC3C2×C4×C9⋊C9
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C22×C32 ◁ C22×C9⋊C9

412 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 182 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) = 648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1805);