Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×Q32 |
| unambiguous semidirect product | (C22×Q32)⋊C32 |
| unambiguous semidirect product | (C22×C3×Q32)⋊C3 |
| Fitting | C22×C3×Q32 ⋊ C3 |
| Sylow | C22×Q32 ⋊ C32 |
248 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153639);