Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C11 |
| direct product | C7×C5⋊(C11⋊D11) |
| unambiguous semidirect product | C5⋊(C7×C11⋊D11) |
| unambiguous semidirect product | C11⋊(C7×D55) |
| Fitting, socle, Hall | C5×C7×C112 ⋊ C2 |
| derived, Hall | C5×C112 ⋊ C2×C7 |
| Hall | C7×C112 ⋊ D5 |
| Sylow | C112 ⋊ C7×D5 |
| Hall | C5×C7 ⋊ C11⋊D11 |
| Sylow | C5 ⋊ C7×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C5⋊(C11⋊D11) |
| commutator, hypocenter | C5×C112 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C112 | C2 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C7 | |
112 conjugacy classes of subgroups.
2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 51);