Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×(C19⋊C3)⋊Dic19 |
| unambiguous semidirect product | (C19⋊C3)⋊(C5×Dic19) |
| derived, Sylow | C192 ⋊ C3×C4×C5 |
| Hall | C5×C19⋊Dic19 ⋊ C3 |
| Hall | C5×C19×C19⋊C3 ⋊ C4 |
| Hall | C5×C192 ⋊ C3×C4 |
| Hall | C19⋊Dic19 ⋊ C3×C5 |
| Hall | C19×C19⋊C3 ⋊ C4×C5 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1140 |
900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 55);