Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D17×D85 |
| unambiguous semidirect product | (C5×D17)⋊(C3×D17) |
| unambiguous semidirect product | (C17×D17)⋊(C3×D5) |
| Fitting, socle, Hall | C3×C5×C172 ⋊ C22 |
| derived, Hall | C5×C172 ⋊ C22×C3 |
| Hall | C3×C172 ⋊ C2×D5 |
| Sylow | C172 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ D172 |
| Sylow | C5 ⋊ C3×D172 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D17×D85 |
| commutator, cosocle, hypocenter | C5×C172 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C22 |
| LCS | G ▷ C5×C172 | |
| UCS | C1 ◁ C3 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 510 |
1320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 97);