Finite Group DatabasebetaFinite Group Databasebeta| order | 10266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊AGL(1,𝔽59) |
| unambiguous semidirect product | D177⋊C29 |
| unambiguous semidirect product | (C59⋊C29)⋊D3 |
| Fitting, socle, derived, Hall | C3×C59 ⋊ C2×C29 |
| Hall | C3×C59⋊C29 ⋊ C2 |
| Hall | C59⋊C29 ⋊ D3 |
| Hall | D177 ⋊ C29 |
| Sylow | C59 ⋊ D3×C29 |
| Sylow | C3 ⋊ AGL(1,𝔽59) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C59 | C2×C29 |
| LCS | G ▷ C3×C59 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,59|b^a=b^2,d^a=d^58,d^c=d^490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10266, 12);