Finite Group DatabasebetaFinite Group Databasebeta| order | 5658 |
| automorphism | Aut(G) order 4979040 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2829 |
| unambiguous semidirect product | C3⋊D943 |
| unambiguous semidirect product | C23⋊D123 |
| unambiguous semidirect product | C41⋊D69 |
| Fitting, socle, derived, Hall | C3×C23×C41 ⋊ C2 |
| Hall | C23×C41 ⋊ D3 |
| Hall | C3×C41 ⋊ D23 |
| Hall | C3×C23 ⋊ D41 |
| Sylow | C41 ⋊ D69 |
| Sylow | C23 ⋊ D123 |
| Sylow | C3 ⋊ D943 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C23×C41 | C2 |
| LCS | G ▷ C3×C23×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,41|b^a=b^2,c^a=c^22,d^a=d^401416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D41×D69, D23×D123, D3×D943, … |
| maximal normal subgroup of | D41×D69, D23×D123, D3×D943, … |
| maximal quotient of | Dic2829, C2×D2829, D8487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5658, 8);