Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #67180 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C4⋊(C3⋊D15) |
| Fitting | C22×C32×C4×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×D20 |
| Sylow | C5 ⋊ C22×C4⋊(C3⋊D3) |
1416 conjugacy classes of subgroups; only the 375 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 375 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5822);