Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#11765919⋊C7 |
| unambiguous semidirect product | (C4×#11765919)⋊C7 |
| Fitting, Hall | C4×C127 ⋊ C7×C9 |
| derived, Sylow | C127 ⋊ C4×C7×C9 |
| Hall | C4×#11765919 ⋊ C7 |
| Hall | C4×C127⋊C7 ⋊ C9 |
| Hall | #11765919 ⋊ C4×C7 |
| Hall | C127⋊C7 ⋊ C4×C9 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 508 |
260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 82);