Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C7⋊AGL(1,𝔽11) |
| unambiguous semidirect product | C7⋊(C11×AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊(C11×D7) |
| unambiguous semidirect product | D77⋊(C5×C11) |
| Fitting, socle, Hall | C7×C112 ⋊ C2×C5 |
| derived | C7×C11 ⋊ C2×C5×C11 |
| Hall | C7×C11×C11⋊C5 ⋊ C2 |
| Hall | C11×D77 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ D7 |
| Sylow | C112 ⋊ C5×D7 |
| Sylow | C7 ⋊ C11×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C7⋊AGL(1,𝔽11) |
| commutator, hypocenter | C7×C11 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112 | C2×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C11 | |
34 conjugacy classes of subgroups.
352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 25);