Finite Group DatabasebetaFinite Group Databasebeta| order | 5742 |
| automorphism | Aut(G) order 4823280 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2871 |
| unambiguous semidirect product | C9⋊D319 |
| unambiguous semidirect product | C11⋊D261 |
| unambiguous semidirect product | C29⋊D99 |
| Fitting, derived, Hall | C9×C11×C29 ⋊ C2 |
| Hall | C11×C29 ⋊ D9 |
| Hall | C9×C29 ⋊ D11 |
| Hall | C9×C11 ⋊ D29 |
| Sylow | C29 ⋊ D99 |
| Sylow | C11 ⋊ D261 |
| Sylow | C9 ⋊ D319 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C11×C29 | C2 |
| Frattini | C3 | D957 |
| socle | C3×C11×C29 | D3 |
| LCS | G ▷ C9×C11×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,29,3|b^3=e^2,b^a=b^2e,c^a=c^10,d^a=d^28,e^a=e^21437 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D99, D11×D261, D9×D319, … |
| maximal normal subgroup of | D29×D99, D11×D261, D9×D319, … |
| maximal quotient of | Dic2871, C2×D2871, C5×D2871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5742, 8);