Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| direct product | Q16×Q8⋊C9 |
| unambiguous semidirect product | (Q8×Q16)⋊C9 |
| Sylow | Q8×Q16 ⋊ C9 |
203 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1152 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153620);