Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C4×C5×C3⋊D3 |
| Fitting | C22×C32×C4×C5 ⋊ C2 |
| derived, Sylow | C32 ⋊ C23×C4×C5 |
| Hall | C32×C5 ⋊ C23×C4 |
1416 conjugacy classes of subgroups; only the 506 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 506 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5806);