Finite Group DatabasebetaFinite Group Databasebeta| order | 8670 |
| isoclinism | isoclinic class of D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×D85 |
| unambiguous semidirect product | C5⋊(C3×C17×D17) |
| unambiguous semidirect product | C17⋊(C3×D5×C17) |
| Fitting, socle, Hall | C3×C5×C172 ⋊ C2 |
| derived | C5×C17 ⋊ C2×C3×C17 |
| Hall | C5×C172 ⋊ C2×C3 |
| Hall | C3×C172 ⋊ D5 |
| Sylow | C172 ⋊ C3×D5 |
| Hall | C3×C5 ⋊ C17×D17 |
| Sylow | C5 ⋊ C3×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | D85 |
| commutator, hypocenter | C5×C17 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C3×C17 | |
64 conjugacy classes of subgroups.
2244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×#66775, C3×C17×#66776, C3×#19153615, … |
| maximal normal subgroup of | C3×C17×#66775, C3×C17×#66776, C3×#19153615, … |
| maximal quotient of | C3×C17×Dic85, C2×C3×C17×D85, C9×C17×D85, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8670, 19);