Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C9 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C9×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C42×C9) |
| Fitting | C2×C4×C5×C9 ⋊ C4 |
| derived, Sylow | C5 ⋊ C2×C42×C9 |
| Hall | C5×C9 ⋊ C2×C42 |
324 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1546);