Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | D3×C3⋊(C3⋊Dic9) |
| unambiguous semidirect product | (C3×D3)⋊(C3⋊Dic9) |
| unambiguous semidirect product | (D3×C9)⋊(C3⋊Dic3) |
| derived, Sylow | C33×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C3⋊(C3⋊D9) |
| commutator, hypocenter | C33×C9 | C2×C4 |
| Frattini | C2×C3 | D3×C3⋊(C3⋊D3) |
| Fitting, cosocle | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| prime radical | C2×C33×D3 | D3 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
1244 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3161);