Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D121⋊C5 |
| unambiguous semidirect product | D121⋊(C5×C7) |
| unambiguous semidirect product | (C121⋊C5)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D121)⋊C5 |
| Fitting, Hall | C7×C121 ⋊ C2×C5 |
| derived, Sylow | C121 ⋊ C2×C5×C7 |
| Hall | C7×C121⋊C5 ⋊ C2 |
| Hall | C7×D121 ⋊ C5 |
| Hall | C121⋊C5 ⋊ C2×C7 |
| Hall | D121 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D121⋊C5 |
| commutator, hypocenter | C121 | C2×C5×C7 |
| Frattini | C11 | C7×AGL(1,𝔽11) |
| Fitting | C7×C121 | C2×C5 |
| socle | C7×C11 | AGL(1,𝔽11) |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
154 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D121⋊C5, C2×C7×D121⋊C5, C3×C7×D121⋊C5, … |
| maximal normal subgroup of | D7×D121⋊C5, C2×C7×D121⋊C5, C3×C7×D121⋊C5, … |
| maximal quotient of | C7×Dic121⋊C5, C2×C7×D121⋊C5, C3×C7×D121⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 2);