Finite Group DatabasebetaFinite Group Databasebeta| order | 20724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic157⋊C3 |
| unambiguous semidirect product | Dic157⋊(C3×C11) |
| unambiguous semidirect product | (C11×Dic157)⋊C3 |
| derived, Sylow | C157 ⋊ C3×C4×C11 |
| Hall | C11×Dic157 ⋊ C3 |
| Hall | C11×C157⋊C3 ⋊ C4 |
| Hall | C11×C157 ⋊ C3×C4 |
| Hall | Dic157 ⋊ C3×C11 |
| Hall | C157⋊C3 ⋊ C4×C11 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6908 |
704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20724, 10);