Finite Group DatabasebetaFinite Group Databasebeta| order | 17986 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D529 |
| unambiguous semidirect product | C529⋊(C2×C17) |
| Fitting, Hall | C17×C529 ⋊ C2 |
| derived, Sylow | C529 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D529 |
| commutator, cosocle, hypocenter | C529 | C2×C17 |
| Frattini | C23 | C17×D23 |
| Fitting | C17×C529 | C2 |
| socle | C17×C23 | D23 |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C17 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8993 |
4522 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D529, C2×C17×D529 |
| maximal normal subgroup of | D17×D529, C2×C17×D529 |
| maximal quotient of | C17×Dic529, C2×C17×D529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17986, 3);