Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C4×(C211⋊C3)⋊C7 |
| unambiguous semidirect product | (C4×C211⋊C3)⋊C7 |
| unambiguous semidirect product | (C4×C211⋊C7)⋊C3 |
| Fitting, Hall | C4×C211 ⋊ C3×C7 |
| derived, Sylow | C211 ⋊ C3×C4×C7 |
| Hall | C4×C211⋊C7 ⋊ C3 |
| Hall | C4×C211⋊C3 ⋊ C7 |
| Hall | C211⋊C7 ⋊ C3×C4 |
| Hall | C211⋊C3 ⋊ C4×C7 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 844 |
124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 7);