Finite Group DatabasebetaFinite Group Databasebeta| order | 30690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C11×C31⋊C9 |
| unambiguous semidirect product | (C2×C5×C31)⋊(C9×C11) |
| unambiguous semidirect product | (C2×C5×C11×C31)⋊C9 |
| derived, Sylow | C31 ⋊ C2×C5×C9×C11 |
| Hall | C2×C5×C11×C31 ⋊ C9 |
| Hall | C5×C11×C31 ⋊ C2×C9 |
| Hall | C2×C11×C31 ⋊ C5×C9 |
| Hall | C11×C31 ⋊ C2×C5×C9 |
| Hall | C2×C5×C31 ⋊ C9×C11 |
| Hall | C5×C31 ⋊ C2×C9×C11 |
| Hall | C2×C31 ⋊ C5×C9×C11 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30690 |
4290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30690, 8);