Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D127⋊C7 |
| unambiguous semidirect product | (C2×C9×D127)⋊C7 |
| Fitting | C2×C9×C127 ⋊ C2×C7 |
| derived, Sylow | C127 ⋊ C22×C7×C9 |
| Hall | C9×C127⋊C7 ⋊ C22 |
| Hall | C2×C9×D127 ⋊ C7 |
| Hall | C9×C127 ⋊ C22×C7 |
| Hall | C127⋊C7 ⋊ C22×C9 |
| Hall | C2×D127 ⋊ C7×C9 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2286 |
414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 37);