Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C25×(C3⋊D3)⋊D23 |
| unambiguous semidirect product | (C3⋊D3)⋊(C25×D23) |
| unambiguous semidirect product | D69⋊(D3×C25) |
| Fitting, Hall | C32×C23×C25 ⋊ C22 |
| derived, Hall | C32×C23 ⋊ C22×C25 |
| Hall | C23×C25 ⋊ D32 |
| Hall | C32×C25 ⋊ C2×D23 |
| Sylow | C23 ⋊ D32×C25 |
| Sylow | C32 ⋊ C2×C25×D23 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3450 |
1875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 81);