Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×(C127⋊C3)⋊C4 |
| derived, Sylow | C127 ⋊ C32×C4×C7 |
| Hall | C3×C7×C127⋊C3 ⋊ C4 |
| Hall | C7×Dic127 ⋊ C32 |
| Hall | C3×C127⋊C3 ⋊ C4×C7 |
| Hall | C7×C127 ⋊ C32×C4 |
| Hall | Dic127 ⋊ C32×C7 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10668 |
1134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 109);