Finite Group DatabasebetaFinite Group Databasebeta| order | 15540 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C7×Dic37 |
| derived, Sylow | C37 ⋊ C3×C4×C5×C7 |
| Hall | C3×C5×C7×C37 ⋊ C4 |
| Hall | C5×C7×C37 ⋊ C3×C4 |
| Hall | C3×C7×C37 ⋊ C4×C5 |
| Hall | C3×C5×C37 ⋊ C4×C7 |
| Hall | C7×C37 ⋊ C3×C4×C5 |
| Hall | C5×C37 ⋊ C3×C4×C7 |
| Hall | C3×C37 ⋊ C4×C5×C7 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15540 |
4200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15540, 6);