Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C1 |
| direct product | D3×C9×C37 |
| unambiguous semidirect product | C3⋊(C2×C9×C37) |
| Fitting, Hall | C3×C9×C37 ⋊ C2 |
| derived | C3 ⋊ C2×C9×C37 |
| Sylow | C3×C9 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C37 | D3 |
| commutator, hypocenter | C3 | C2×C9×C37 |
| Frattini | C3 | C3×D3×C37 |
| Fitting | C3×C9×C37 | C2 |
| socle | C32×C37 | C2×C3 |
| prime radical | C3×D3×C37 | C3 |
| cosocle | C32 | C2×C3×C37 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C9×C37 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 666 |
999 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 35);