Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#11765917⋊D7 |
| unambiguous semidirect product | (C2×#11765917)⋊D7 |
| derived, Hall | C7×C127 ⋊ C22×C9 |
| Hall | C7×#11765917 ⋊ C22 |
| Hall | C2×D889 ⋊ C9 |
| Hall | #11765917 ⋊ C2×D7 |
| Sylow | C127 ⋊ C2×C9×D7 |
| Sylow | C7 ⋊ C2×#11765917⋊C2 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16002 |
972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 55);