Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊Dic45 |
| unambiguous semidirect product | C3⋊(C3×Dic45) |
| derived | C3×C5×C9 ⋊ C3×C4 |
| Hall | C32×C5×C9 ⋊ C4 |
| Sylow | C32×C9 ⋊ Dic5 |
| Sylow | C5 ⋊ C3×C3⋊Dic9 |
180 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 540 |
414 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 247);