Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C17 |
| direct product | D15×C17⋊D17 |
| Fitting, socle, derived, Hall | C3×C5×C172 ⋊ C22 |
| 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, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C172 | C22 |
| LCS | G ▷ C3×C5×C172 | |
| UCS | C1 | |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4335 |
1314 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 122);