Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of 3−1+2⋊D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | 3−1+2⋊D37 |
| Fitting, Hall | 3−1+2×C37 ⋊ C2 |
| derived | C9×C37 ⋊ C2×C3 |
| Sylow | C37 ⋊ AGL(1,ℤ/9) |
| Sylow | 3−1+2 ⋊ D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C9×C37 | C2×C3 |
| Frattini | C3 | C3×D111 |
| Fitting | 3−1+2×C37 | C2 |
| socle | C3×C37 | C3×D3 |
| LCS | G ▷ C9×C37 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 333 |
Polycyclic presentation:
2,3^2,37,3|c^3=e^2,c^a=c^2e,d^a=d^36,e^a=e^2,c^b=ce208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 41);