Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| isoclinism | isoclinic class of #66774 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×#66774 |
| Fitting, socle, Hall | C3×C5×C172 ⋊ C4 |
| derived | C5×C17 ⋊ C3×C4×C17 |
| Hall | C5×C172 ⋊ C3×C4 |
| Hall | C3×C172 ⋊ AGL(1,𝔽5) |
| Sylow | C172 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ C17×Dic17 |
| Sylow | C5 ⋊ C3×C17×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | #66774 |
| commutator, hypocenter | C5×C17 | C3×C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C4 |
| prime radical | C3×D5×C172 | C2 |
| cosocle | D5×C17 | C2×C3×C17 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C3×C17 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 510 |
1887 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 84);