Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| isoclinism | isoclinic class of D171 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D171 |
| unambiguous semidirect product | C9⋊(D19×C49) |
| unambiguous semidirect product | C19⋊(D9×C49) |
| Fitting, Hall | C9×C19×C49 ⋊ C2 |
| derived, Hall | C9×C19 ⋊ C2×C49 |
| Hall | C19×C49 ⋊ D9 |
| Hall | C9×C49 ⋊ D19 |
| Sylow | C19 ⋊ D9×C49 |
| Sylow | C9 ⋊ D19×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D171 |
| commutator, hypocenter | C9×C19 | C2×C49 |
| Frattini | C3×C7 | C7×D57 |
| Fitting | C9×C19×C49 | C2 |
| socle | C3×C7×C19 | D3×C7 |
| prime radical | C7×D171 | C7 |
| cosocle | C7×C9×C19 | C2×C7 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C49 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8379 |
4263 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D19×C49, D49×D171, D171⋊D49, … |
| maximal normal subgroup of | D9×D19×C49, D49×D171, D171⋊D49, … |
| maximal quotient of | C49×Dic171, C2×C49×D171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 22);