Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#67×3−1+2 |
| unambiguous semidirect product | (C9×#67)⋊C32 |
| Fitting | C22×C32×3−1+2 ⋊ C2 |
| Sylow | C32×3−1+2 ⋊ D4 |
1138 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | 3−1+2×#3811, C3×#67×AGL(1,ℤ/9), #72228838, … |
| maximal normal subgroup of | 3−1+2×#3811, C3×#67×AGL(1,ℤ/9), #72228838, … |
| maximal quotient of | C3×#14517439, 3−1+2×#611⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3298);