Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C7×C22⋊#11765917 |
| unambiguous semidirect product | C22⋊(C7×#11765917) |
| derived, Hall | C22×C127 ⋊ C7×C9 |
| Hall | C22×C7×C127 ⋊ C9 |
| Hall | C7×C127 ⋊ C22⋊C9 |
| Sylow | C127 ⋊ C7×C22⋊C9 |
| Hall | C22×C7 ⋊ #11765917 |
| Sylow | C22 ⋊ C7×#11765917 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16002 |
3612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 67);