Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#13181892⋊C2 |
| unambiguous semidirect product | #13181892⋊(C2×C5) |
| unambiguous semidirect product | ((C17⋊D17)⋊C3)⋊(C2×C5) |
| Fitting, socle, Hall | C5×C172 ⋊ C2×D3 |
| derived, Hall | C172⋊C3 ⋊ C22×C5 |
| Hall | C5×C172⋊C3 ⋊ C22 |
| Sylow | C172 ⋊ C2×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #13181892⋊C2 |
| commutator, cosocle, hypocenter | C172⋊C3 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C172 | C2×D3 |
| LCS | G ▷ C172⋊C3 | |
| UCS | C1 ◁ C5 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 255 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 56);