Finite Group DatabasebetaFinite Group Databasebeta| order | 16762 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D29×C289 |
| unambiguous semidirect product | C29⋊(C2×C289) |
| Fitting, Hall | C29×C289 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D29 |
| commutator, hypocenter | C29 | C2×C289 |
| Frattini | C17 | C17×D29 |
| Fitting | C29×C289 | C2 |
| socle, cosocle | C17×C29 | C2×C17 |
| prime radical | C17×D29 | C17 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8381 |
4624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1181×C289, #45692825, D29×D289, … |
| maximal normal subgroup of | #1181×C289, #45692825, D29×D289, … |
| maximal quotient of | Dic29×C289, C2×D29×C289 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16762, 3);