Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic5×SL(2,𝔽3) |
| unambiguous semidirect product | (Q8×Dic5)⋊C32 |
| unambiguous semidirect product | (C3×Q8×Dic5)⋊C3 |
| derived | C5×Q8 ⋊ C32×C4 |
| Hall | Q8×Dic5 ⋊ C32 |
| Sylow | C5 ⋊ C3×C4×SL(2,𝔽3) |
164 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2541);