Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C23 · Schur multiplier (H2) = C2 |
| direct product | C9×D52×C23 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C9×C23) |
| Fitting, Hall | C52×C9×C23 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C9×C23 |
| Hall | C52×C23 ⋊ C22×C9 |
| Hall | C52×C9 ⋊ C22×C23 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2070 |
3312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 132);