Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of C3⋊D333 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D333 |
| unambiguous semidirect product | C9⋊D111 |
| unambiguous semidirect product | C37⋊(C3⋊D9) |
| Fitting, derived, Hall | C3×C9×C37 ⋊ C2 |
| Sylow | C37 ⋊ C3⋊D9 |
| Sylow | C3×C9 ⋊ D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C9×C37 | C2 |
| Frattini | C3 | C3⋊D111 |
| socle | C32×C37 | D3 |
| LCS | G ▷ C3×C9×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 999 |
Polycyclic presentation:
2,3^2,37,3|c^3=e^2,b^a=b^2,c^a=c^2e,d^a=d^36,e^a=e^2501 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 44);