Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×C3⋊C16 |
| derived | C3×C5 ⋊ C2×C3×C16 |
| Hall | C32×C5 ⋊ C2×C16 |
| Sylow | C32 ⋊ D5×C16 |
| Sylow | C5 ⋊ C2×C3×C3⋊C16 |
134 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 949);