Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C17 |
| direct product | C2×C5×(C17⋊D17)⋊C3 |
| unambiguous semidirect product | (C2×C17⋊D17)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C17⋊D17)⋊C3 |
| Fitting, socle | C2×C5×C172 ⋊ C2×C3 |
| derived, Sylow | C172 ⋊ C22×C3×C5 |
| Hall | C2×C5×C17⋊D17 ⋊ C3 |
| Hall | C5×C172⋊C3 ⋊ C22 |
| Hall | C5×C172 ⋊ C22×C3 |
| Hall | C2×C17⋊D17 ⋊ C3×C5 |
| Hall | C172⋊C3 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | (C17⋊D17)⋊C3 |
| commutator, cosocle, hypocenter | C172 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C172 | C2×C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2×C5 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 510 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 72);