Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D609 |
| unambiguous semidirect product | C3⋊(C7×D203) |
| unambiguous semidirect product | C7⋊(C7×D87) |
| Fitting, socle, Hall | C3×C72×C29 ⋊ C2 |
| derived | C3×C7×C29 ⋊ C2×C7 |
| Hall | C72×C29 ⋊ D3 |
| Hall | C3×C72 ⋊ D29 |
| Hall | C3×C29 ⋊ C7×D7 |
| Sylow | C72 ⋊ D87 |
| Sylow | C29 ⋊ C7×D21 |
| Sylow | C3 ⋊ C7×D203 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D609 |
| commutator, hypocenter | C3×C7×C29 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C29 | C2 |
| LCS | G ▷ C3×C7×C29 | |
| UCS | C1 ◁ C7 | |
44 conjugacy classes of subgroups.
2142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D21×D29, C7×D7×D87, D3×C7×D203, … |
| maximal normal subgroup of | C7×D21×D29, C7×D7×D87, D3×C7×D203, … |
| maximal quotient of | C7×Dic609, C2×C7×D609, C7×D1827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 60);