Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D289 |
| unambiguous semidirect product | (D5×C289)⋊(C2×C3) |
| unambiguous semidirect product | (C5×D289)⋊(C2×C3) |
| unambiguous semidirect product | D1445⋊(C2×C3) |
| Fitting, Hall | C3×C5×C289 ⋊ C22 |
| derived, Hall | C5×C289 ⋊ C22×C3 |
| Hall | C3×C289 ⋊ C2×D5 |
| Sylow | C289 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ C2×D289 |
| Sylow | C5 ⋊ C2×C3×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D289 |
| commutator, cosocle, hypocenter | C5×C289 | C22×C3 |
| Frattini | C17 | C3×D5×D17 |
| Fitting | C3×C5×C289 | C22 |
| socle | C3×C5×C17 | C2×D17 |
| LCS | G ▷ C5×C289 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4335 |
1752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 22);