Finite Group DatabasebetaFinite Group Databasebeta| order | 15372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#21440255 |
| derived, Hall | C7×C61 ⋊ C22×C9 |
| Hall | #16838635 ⋊ C22 |
| Hall | C2×D7×C61 ⋊ C9 |
| Sylow | C61 ⋊ C2×D7⋊C9 |
| Hall | C2×D7 ⋊ C61⋊C9 |
| Sylow | C7 ⋊ C22×C61⋊C9 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7686 |
642 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15372, 42);