Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D385 |
| unambiguous semidirect product | C5⋊(C11×D77) |
| unambiguous semidirect product | C7⋊(C11×D55) |
| unambiguous semidirect product | C11⋊(C11×D35) |
| Fitting, socle, Hall | C5×C7×C112 ⋊ C2 |
| derived | C5×C7×C11 ⋊ C2×C11 |
| Hall | C7×C112 ⋊ D5 |
| Hall | C5×C112 ⋊ D7 |
| Sylow | C112 ⋊ D35 |
| Hall | C5×C7 ⋊ C11×D11 |
| Sylow | C7 ⋊ C11×D55 |
| Sylow | C5 ⋊ C11×D77 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D385 |
| commutator, hypocenter | C5×C7×C11 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C112 | C2 |
| LCS | G ▷ C5×C7×C11 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
2134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D35, D11×D385, #30683910, … |
| maximal normal subgroup of | C11×D11×D35, D11×D385, #30683910, … |
| maximal quotient of | C11×Dic385, C2×C11×D385, C3×C11×D385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 53);