Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×D15×D17 |
| unambiguous semidirect product | (C3×D17)⋊(D5×C17) |
| unambiguous semidirect product | (C5×D17)⋊(D3×C17) |
| Fitting, socle, Hall | C3×C5×C172 ⋊ C22 |
| derived | C3×C5×C17 ⋊ C22×C17 |
| Hall | C5×C172 ⋊ C2×D3 |
| Hall | C3×C172 ⋊ C2×D5 |
| Sylow | C172 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×C17×D17 |
| Sylow | C5 ⋊ D3×C17×D17 |
| Sylow | C3 ⋊ D5×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D15×D17 |
| commutator, cosocle, hypocenter | C3×C5×C17 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C22 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C17 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 510 |
1530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 118);