Finite Group DatabasebetaFinite Group Databasebeta| order | 10266 |
| automorphism | Aut(G) order 16671984 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5133 |
| unambiguous semidirect product | C3⋊D1711 |
| unambiguous semidirect product | C29⋊D177 |
| unambiguous semidirect product | C59⋊D87 |
| Fitting, socle, derived, Hall | C3×C29×C59 ⋊ C2 |
| Hall | C29×C59 ⋊ D3 |
| Hall | C3×C59 ⋊ D29 |
| Hall | C3×C29 ⋊ D59 |
| Sylow | C59 ⋊ D87 |
| Sylow | C29 ⋊ D177 |
| Sylow | C3 ⋊ D1711 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C29×C59 | C2 |
| LCS | G ▷ C3×C29×C59 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,59|b^a=b^2,c^a=c^28,d^a=d^582568 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D87, D29×D177, D3×D1711, … |
| maximal normal subgroup of | D59×D87, D29×D177, D3×D1711, … |
| maximal quotient of | Dic5133, C2×D5133, D15399, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10266, 9);