Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D5⋊(C9⋊C8) |
| unambiguous semidirect product | D5⋊(C2×C9⋊C8) |
| derived, Hall | C5×C9 ⋊ C22×C8 |
| Sylow | C9 ⋊ C2×D5⋊C8 |
| Sylow | C5 ⋊ C22×C9⋊C8 |
228 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1556);