Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C9⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C3×Dic9) |
| Fitting | C2×C3×C5×C9 ⋊ C4 |
| derived | C5×C9 ⋊ C2×C3×C4 |
| Hall | C3×C5×C9 ⋊ C2×C4 |
| Sylow | C3×C9 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C3×Dic9 |
116 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 318);