Finite Group DatabasebetaFinite Group Databasebeta| order | 19890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D255 |
| unambiguous semidirect product | C3⋊(C3×C13×D85) |
| unambiguous semidirect product | C5⋊(C3×C13×D51) |
| unambiguous semidirect product | C17⋊(C3×C13×D15) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D255 |
| commutator, cosocle, hypocenter | C3×C5×C17 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C13×C17 | C2 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C3×C13 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6630 |
5031 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19890, 52);