Finite Group DatabasebetaFinite Group Databasebeta| order | 8973 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C997⋊C9 |
| derived, Sylow | C997 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C997⋊C3 |
| commutator, hypocenter | C997 | C9 |
| Fitting, socle | C3×C997 | C3 |
| LCS | G ▷ C997 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,997|a^3=b,c^a=c^3041005 conjugacy classes — view the full character table.
| maximal subgroup of | D997⋊C9, C2×C997⋊C9, C9×C997⋊C3, … |
| maximal normal subgroup of | D997⋊C9, C2×C997⋊C9, C9×C997⋊C3, … |
| maximal quotient of | C2×C997⋊C9, C997⋊C27, C3×C997⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8973, 1);