Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D29⋊C49) |
| unambiguous semidirect product | D87⋊C49 |
| unambiguous semidirect product | (C29⋊C49)⋊D3 |
| derived, Hall | C3×C29 ⋊ C2×C49 |
| Hall | C3×C29⋊C49 ⋊ C2 |
| Hall | C29⋊C49 ⋊ D3 |
| Hall | D87 ⋊ C49 |
| Sylow | C29 ⋊ D3×C49 |
| Sylow | C3 ⋊ D29⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | C3⋊(D29⋊C7) |
| commutator, hypocenter | C3×C29 | C2×C49 |
| Fitting, socle | C3×C7×C29 | C2×C7 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,3,29,7|b^7=e,c^a=c^2,d^a=d^28,d^b=d^23189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 4);