Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C3×C5 |
| direct product | C23×#11744708 |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C4 |
| derived, Hall | C32×C52 ⋊ C4×C23 |
| Hall | C52×C23 ⋊ #157 |
| Hall | C32×C23 ⋊ #1044 |
| Sylow | C52 ⋊ C23×#157 |
| Sylow | C32 ⋊ C23×#1044 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
1380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 261);