Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,ℤ/8)×C22⋊C9 |
| unambiguous semidirect product | (C22×AGL(1,ℤ/8))⋊C9 |
| Sylow | C22×AGL(1,ℤ/8) ⋊ C9 |
732 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153806);