Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D32×3−1+2 |
| unambiguous semidirect product | (C3×D3)⋊(C22×3−1+2) |
| unambiguous semidirect product | (C2×D32×C9)⋊C3 |
| Fitting | C2×C32×3−1+2 ⋊ C22 |
| Sylow | C32×3−1+2 ⋊ C23 |
848 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 196 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D32×AGL(1,ℤ/9), 3−1+2×#3811, C2×D3×#92265, … |
| maximal normal subgroup of | C2×D32×AGL(1,ℤ/9), 3−1+2×#3811, #72228856, … |
| maximal quotient of | 3−1+2×#3811, C2×D3×#92265, D33×3−1+2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3695);