Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#6192⋊C3 |
| unambiguous semidirect product | #6192⋊C32 |
| unambiguous semidirect product | (C3×#6192)⋊C3 |
| Sylow | C32×3−1+2 ⋊ D4 |
598 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67×AGL(1,ℤ/9), #72228852, #72228864, … |
| maximal normal subgroup of | C3×#67×AGL(1,ℤ/9), #72228852, #72228864, … |
| maximal quotient of | #72228945, C3×#14516829 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3029);