Finite Group DatabasebetaFinite Group Databasebeta| order | 5982 |
| automorphism | Aut(G) order 5958072 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2991 |
| unambiguous semidirect product | C3⋊D997 |
| unambiguous semidirect product | C997⋊D3 |
| Fitting, socle, derived, Hall | C3×C997 ⋊ C2 |
| Sylow | C997 ⋊ D3 |
| Sylow | C3 ⋊ D997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C997 | C2 |
| LCS | G ▷ C3×C997 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,997|b^a=b^2,c^a=c^9961497 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D997, C2×D2991, D8973, … |
| maximal normal subgroup of | D3×D997, C2×D2991, C3⋊(D997⋊C3), … |
| maximal quotient of | Dic2991, C2×D2991, D8973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5982, 5);