Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×#11765917⋊C2 |
| derived, Sylow | C127 ⋊ C22×C7×C9 |
| Hall | C7×#11765917 ⋊ C22 |
| Hall | C2×C7×D127 ⋊ C9 |
| Hall | #11765917 ⋊ C22×C7 |
| Hall | C7×C127 ⋊ C22×C9 |
| Hall | C2×D127 ⋊ C7×C9 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16002 |
1134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 45);