Finite Group DatabasebetaFinite Group Databasebeta| order | 5982 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D997⋊C3 |
| unambiguous semidirect product | (C997⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C997 ⋊ C2×C3 |
| Hall | C997⋊C3 ⋊ C2 |
| Hall | D997 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C997 | C2×C3 |
| LCS | G ▷ C997 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,997|c^a=c^996,c^b=c^304172 conjugacy classes — view the full character table.
| maximal subgroup of | #16860614⋊C3, C2×D997⋊C3, C3×D997⋊C3, … |
| maximal normal subgroup of | #16860614⋊C3, C2×D997⋊C3, C3×D997⋊C3, … |
| maximal quotient of | Dic997⋊C3, C2×D997⋊C3, D997⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5982, 1);