Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3×C127⋊C7 |
| unambiguous semidirect product | C3⋊(C3×C4×C127⋊C7) |
| unambiguous semidirect product | (C3×Dic3×C127)⋊C7 |
| derived | C3×C127 ⋊ C3×C4×C7 |
| Hall | C32×C127⋊C7 ⋊ C4 |
| Hall | C3×Dic3×C127 ⋊ C7 |
| Hall | C32×C127 ⋊ C4×C7 |
| Sylow | C127 ⋊ C3×C7×Dic3 |
| Sylow | C32 ⋊ C4×C127⋊C7 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1524 |
450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 101);