Finite Group DatabasebetaFinite Group Databasebeta| order | 17690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1769 |
| unambiguous semidirect product | C29⋊(C5×D61) |
| Fitting, socle, Hall | C5×C29×C61 ⋊ C2 |
| derived, Hall | C29×C61 ⋊ C2×C5 |
| Hall | C5×C61 ⋊ D29 |
| Hall | C5×C29 ⋊ D61 |
| Sylow | C61 ⋊ C5×D29 |
| Sylow | C29 ⋊ C5×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1769 |
| commutator, cosocle, hypocenter | C29×C61 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C61 | C2 |
| LCS | G ▷ C29×C61 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8845 |
4430 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20296685, C5×#20296686, C5×D29×D61, … |
| maximal normal subgroup of | C5×#20296685, C5×#20296686, C5×D29×D61, … |
| maximal quotient of | C5×Dic1769, C2×C5×D1769 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17690, 5);