Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | Dic9×C127⋊C7 |
| unambiguous semidirect product | C9⋊(C4×C127⋊C7) |
| unambiguous semidirect product | (Dic9×C127)⋊C7 |
| derived, Hall | C9×C127 ⋊ C4×C7 |
| Hall | C9×C127⋊C7 ⋊ C4 |
| Hall | Dic9×C127 ⋊ C7 |
| Sylow | C127 ⋊ C7×Dic9 |
| Sylow | C9 ⋊ C4×C127⋊C7 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4572 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 16);