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D3×Dic3×3−1+2 #14518639

order1944
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2

Aliases

direct productD3×Dic3×3−1+2
unambiguous semidirect product(C3×D3)⋊(C4×3−1+2)
unambiguous semidirect product(D3×C9×Dic3)⋊C3

Splittings

SylowC32×3−1+2 ⋊ C2×C4

Subgroups

subgroupG/H
center, FrattiniC2×C3C32×D32
commutatorC33C2×C32×C4
FittingC2×C32×3−1+2C22
socle, cosocleC2×C33C22×C32
prime radicalC2×C33×D3C2×C3
hypercenterC2×3−1+2D32
hypocenterC32C2×C4×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

532 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 72

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#11757569, D3×(C3⋊AGL(1,ℤ/9))⋊C4, D3×#6192⋊C3, …
maximal normal subgroup ofD3×(C3⋊AGL(1,ℤ/9))⋊C4, D3×#6192⋊C3, D3×#67×3−1+2
maximal quotient ofD3×#11757569

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3033);