Finite Group DatabasebetaFinite Group Databasebeta| order | 8526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D29⋊C7) |
| unambiguous semidirect product | (C29⋊C7)⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D29)⋊C7 |
| unambiguous semidirect product | (C7⋊(D29⋊C7))⋊C3 |
| Fitting, socle, derived | C7×C29 ⋊ C2×C3×C7 |
| Hall | ΓL(1,𝔽8)×C29⋊C7 ⋊ C2 |
| Hall | C7⋊(D29⋊C7) ⋊ C3 |
| Hall | C7×C29⋊C7 ⋊ C2×C3 |
| Sylow | C29 ⋊ C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C29 | C2×C3×C7 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,29|d^a=d^6,e^a=e^28,d^b=d^2,e^c=e^1659 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8526, 18);