Finite Group DatabasebetaFinite Group Databasebeta| order | 8330 |
| isoclinism | isoclinic class of D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D85 |
| unambiguous semidirect product | C5⋊(D17×C49) |
| unambiguous semidirect product | C17⋊(D5×C49) |
| Fitting, Hall | C5×C17×C49 ⋊ C2 |
| derived, Hall | C5×C17 ⋊ C2×C49 |
| Hall | C17×C49 ⋊ D5 |
| Hall | C5×C49 ⋊ D17 |
| Sylow | C17 ⋊ D5×C49 |
| Sylow | C5 ⋊ D17×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D85 |
| commutator, hypocenter | C5×C17 | C2×C49 |
| Frattini | C7 | C7×D85 |
| Fitting | C5×C17×C49 | C2 |
| socle | C5×C7×C17 | C2×C7 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
2156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×#66775, C49×#66776, C49⋊#66775, … |
| maximal normal subgroup of | C49×#66775, C49×#66776, C49⋊#66775, … |
| maximal quotient of | C49×Dic85, C2×C49×D85, C3×C49×D85, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8330, 6);