Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×C4⋊(C3⋊(C3⋊D9)) |
| unambiguous semidirect product | C4⋊(C3×C3⋊(C3⋊D9)) |
| Fitting | C33×C4×C9 ⋊ C2 |
| Sylow | C33×C9 ⋊ D4 |
1244 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 306 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3369);