Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C23×C32 |
| direct product | C22×C3×D3×3−1+2 |
| unambiguous semidirect product | C3⋊(C23×C3×3−1+2) |
| unambiguous semidirect product | (C2×C3)⋊(C22×C3×3−1+2) |
| Fitting | C22×C32×3−1+2 ⋊ C2 |
| Sylow | C32×3−1+2 ⋊ C23 |
1746 conjugacy classes of subgroups; only the 672 normal subgroups are shown.
This group has 1746 conjugacy classes of subgroups — too many to draw. Only its 672 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D3×#6900, C22×D3×C3⋊AGL(1,ℤ/9), C3×D3×#611⋊C3, … |
| maximal normal subgroup of | C22×D3×#6900, C22×D3×C3⋊AGL(1,ℤ/9), C3×D3×#611⋊C3, … |
| maximal quotient of | C22×D3×#6900 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3751);