Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of (C37⋊C3)⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C37⋊C3)⋊D9 |
| Fitting, derived | C9×C37 ⋊ C2×C3 |
| Hall | C9×C37⋊C3 ⋊ C2 |
| Sylow | C37 ⋊ C3×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C37 | C2×C3 |
| Frattini | C3 | C3⋊(D37⋊C3) |
| socle | C3×C37 | C3×D3 |
| LCS | G ▷ C9×C37 | |
| UCS | C1 | |
28 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,d^b=d^1072 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 20);