Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11×C49 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C11×C49 |
| unambiguous semidirect product | C3⋊(C2×C5×C11×C49) |
| Fitting, Hall | C3×C5×C11×C49 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C11×C49 |
| Hall | C3×C11×C49 ⋊ C2×C5 |
| Hall | C3×C5×C49 ⋊ C2×C11 |
| Hall | C3×C5×C11 ⋊ C2×C49 |
| Hall | C3×C49 ⋊ C2×C5×C11 |
| Hall | C3×C11 ⋊ C2×C5×C49 |
| Hall | C3×C5 ⋊ C2×C11×C49 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8085 |
8085 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D11×C49, C5×D3×C11×D49, C5×D3×D539, … |
| maximal normal subgroup of | C5×D3×D11×C49, C5×D3×C11×D49, C5×D3×D539, … |
| maximal quotient of | C5×C11×Dic3×C49, C2×C5×D3×C11×C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 12);