Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C9×D61 |
| Fitting | C2×C7×C9×C61 ⋊ C2 |
| derived, Sylow | C61 ⋊ C22×C7×C9 |
| Hall | C7×C9×C61 ⋊ C22 |
| Hall | C9×C61 ⋊ C22×C7 |
| Hall | C7×C61 ⋊ C22×C9 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7686 |
4032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 70);