Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C5 |
| direct product | C23×C9⋊#1039 |
| unambiguous semidirect product | C9⋊(C23×#1039) |
| derived, Hall | C52×C9 ⋊ C4×C23 |
| Hall | C52×C9×C23 ⋊ C4 |
| Hall | C52×C23 ⋊ Dic9 |
| Hall | C9×C23 ⋊ #1039 |
| Sylow | C52 ⋊ C23×Dic9 |
| Sylow | C9 ⋊ C23×#1039 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20700 |
5244 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 57);