Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×(C61⋊C9)⋊D7 |
| unambiguous semidirect product | (C2×C61⋊C9)⋊D7 |
| derived, Hall | C7×C61 ⋊ C22×C9 |
| Hall | C7×C61⋊C9 ⋊ C22 |
| Hall | C2×D427 ⋊ C9 |
| Hall | C61⋊C9 ⋊ C2×D7 |
| Sylow | C61 ⋊ C2×C9×D7 |
| Sylow | C7 ⋊ C2×D61⋊C9 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7686 |
510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 48);