Finite Group DatabasebetaFinite Group Databasebeta| order | 8470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D7×C121⋊C5 |
| unambiguous semidirect product | C7⋊(C2×C121⋊C5) |
| unambiguous semidirect product | (D7×C121)⋊C5 |
| Fitting, derived, Hall | C7×C121 ⋊ C2×C5 |
| Hall | C7×C121⋊C5 ⋊ C2 |
| Hall | D7×C121 ⋊ C5 |
| Sylow | C121 ⋊ C5×D7 |
| Sylow | C7 ⋊ C2×C121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C121 | C2×C5 |
| Frattini | C11 | D7×C11⋊C5 |
| socle | C7×C11 | C2×C11⋊C5 |
| LCS | G ▷ C7×C121 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
145 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D121⋊C5, C2×D7×C121⋊C5, C3×D7×C121⋊C5, … |
| maximal normal subgroup of | D7×D121⋊C5, C2×D7×C121⋊C5, C3×D7×C121⋊C5, … |
| maximal quotient of | Dic7×C121⋊C5, C2×D7×C121⋊C5, C3×D7×C121⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8470, 3);