Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C127 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic21×C127 |
| unambiguous semidirect product | C3⋊(C3×Dic7×C127) |
| derived | C3×C7 ⋊ C3×C4×C127 |
| Hall | C32×C7×C127 ⋊ C4 |
| Hall | C32×C127 ⋊ Dic7 |
| Hall | C7×C127 ⋊ C3×Dic3 |
| Hall | C32×C7 ⋊ C4×C127 |
| Sylow | C32 ⋊ Dic7×C127 |
| Sylow | C7 ⋊ C3×Dic3×C127 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10668 |
9144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 146);