Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#6705 |
| Fitting | C2×C32×C5×C8 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×M16 |
| Sylow | C32 ⋊ C2×#676 |
| Sylow | C5 ⋊ C2×C3×ΓL(1,𝔽25) |
294 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4314);