Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D847 |
| unambiguous semidirect product | C7⋊(C5×D121) |
| Fitting, Hall | C5×C7×C121 ⋊ C2 |
| derived, Hall | C7×C121 ⋊ C2×C5 |
| Hall | C5×C121 ⋊ D7 |
| Sylow | C121 ⋊ C5×D7 |
| Hall | C5×C7 ⋊ D121 |
| Sylow | C7 ⋊ C5×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D847 |
| commutator, hypocenter | C7×C121 | C2×C5 |
| Frattini | C11 | C5×D77 |
| Fitting | C5×C7×C121 | C2 |
| socle | C5×C7×C11 | D11 |
| LCS | G ▷ C7×C121 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
2125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D7×D121, D5×D847, D35⋊D121, … |
| maximal normal subgroup of | C5×D7×D121, D5×D847, D35⋊D121, … |
| maximal quotient of | C5×Dic847, C2×C5×D847, C3×C5×D847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 8);