Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D9×#360 |
| Fitting | C9×#360 ⋊ C2 |
| Sylow | C9 ⋊ C2×#360 |
348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D9×AGL(1,ℤ/16), AGL(1,ℤ/9)×#360 |
| maximal normal subgroup of | D9×AGL(1,ℤ/16), AGL(1,ℤ/9)×#360 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30822);