Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D637 |
| unambiguous semidirect product | C13⋊(C13×D49) |
| unambiguous semidirect product | C49⋊(C13×D13) |
| Fitting, Hall | C132×C49 ⋊ C2 |
| derived | C13×C49 ⋊ C2×C13 |
| Sylow | C132 ⋊ D49 |
| Sylow | C49 ⋊ C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D637 |
| commutator, cosocle, hypocenter | C13×C49 | C2×C13 |
| Frattini | C7 | C13×D91 |
| Fitting | C132×C49 | C2 |
| socle | C7×C132 | D7 |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C13 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1274 |
4160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D13×D49, D13×D637, D637⋊D13, … |
| maximal normal subgroup of | C13×D13×D49, D13×D637, D637⋊D13, … |
| maximal quotient of | C13×Dic637, C2×C13×D637 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 18);