Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13×C49 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C13×C49 |
| unambiguous semidirect product | C3⋊(C2×C5×C13×C49) |
| Fitting, Hall | C3×C5×C13×C49 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C13×C49 |
| Hall | C3×C13×C49 ⋊ C2×C5 |
| Hall | C3×C5×C49 ⋊ C2×C13 |
| Hall | C3×C5×C13 ⋊ C2×C49 |
| Hall | C3×C49 ⋊ C2×C5×C13 |
| Hall | C3×C13 ⋊ C2×C5×C49 |
| Hall | C3×C5 ⋊ C2×C13×C49 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9555 |
9555 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D13×C49, C5×D3×C13×D49, C5×D3×D637, … |
| maximal normal subgroup of | C5×D3×D13×C49, C5×D3×C13×D49, C5×D3×D637, … |
| maximal quotient of | C5×Dic3×C13×C49, C2×C5×D3×C13×C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 13);