Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C29⋊C49 |
| unambiguous semidirect product | (C2×C29)⋊(C3×C49) |
| unambiguous semidirect product | (C2×C3×C29)⋊C49 |
| derived, Sylow | C29 ⋊ C2×C3×C49 |
| Hall | C2×C3×C29 ⋊ C49 |
| Hall | C3×C29 ⋊ C2×C49 |
| Hall | C2×C29 ⋊ C3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | C29⋊C7 |
| commutator, hypocenter | C29 | C2×C3×C49 |
| Frattini | C7 | C2×C3×C29⋊C7 |
| Fitting, socle | C2×C3×C7×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C3×C7 | |
24 conjugacy classes of subgroups.
462 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 5);