Finite Group DatabasebetaFinite Group Databasebeta| order | 5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1999⋊C3 |
| Fitting, socle, derived, Sylow | C1999 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1999 | C3 |
| LCS | G ▷ C1999 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
3,1999|b^a=b^808669 conjugacy classes — view the full character table.
| maximal subgroup of | D1999⋊C3, C2×C1999⋊C3, #31824623, … |
| maximal normal subgroup of | D1999⋊C3, C2×C1999⋊C3, #31824623, … |
| maximal quotient of | C2×C1999⋊C3, #31824621, C3×C1999⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5997, 1);