Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| direct product | D35×C121 |
| unambiguous semidirect product | C5⋊(D7×C121) |
| unambiguous semidirect product | C7⋊(D5×C121) |
| Fitting, Hall | C5×C7×C121 ⋊ C2 |
| derived, Hall | C5×C7 ⋊ C2×C121 |
| Hall | C7×C121 ⋊ D5 |
| Hall | C5×C121 ⋊ D7 |
| Sylow | C7 ⋊ D5×C121 |
| Sylow | C5 ⋊ D7×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D35 |
| commutator, hypocenter | C5×C7 | C2×C121 |
| Frattini | C11 | C11×D35 |
| Fitting | C5×C7×C121 | C2 |
| socle | C5×C7×C11 | C2×C11 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C121 | |
24 conjugacy classes of subgroups.
2299 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D35×D121, D5×D7×C121, D35⋊D121, … |
| maximal normal subgroup of | D35×D121, D5×D7×C121, D35⋊D121, … |
| maximal quotient of | C121×Dic35, C2×D35×C121, C3×D35×C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 11);