Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×(C11⋊C5)⋊D11 |
| unambiguous semidirect product | (C11⋊C5)⋊(C7×D11) |
| Fitting, socle, Hall | C7×C112 ⋊ C2×C5 |
| derived, Sylow | C112 ⋊ C2×C5×C7 |
| Hall | C7×C11×C11⋊C5 ⋊ C2 |
| Hall | C7×C11⋊D11 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ C2×C7 |
| Hall | C11⋊D11 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C11⋊C5)⋊D11 |
| commutator, hypocenter | C112 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 22);