Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D9×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D9×AGL(1,𝔽5) |
| Fitting | C4×C5×C9 ⋊ C2×C4 |
| derived, Hall | C5×C9 ⋊ C2×C42 |
| Sylow | C9 ⋊ C2×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C42×D9 |
324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D9×AGL(1,𝔽5), C4×AGL(1,𝔽5)×AGL(1,ℤ/9), D9×AGL(1,𝔽5)2, … |
| maximal normal subgroup of | D4×D9×AGL(1,𝔽5), C4×AGL(1,𝔽5)×AGL(1,ℤ/9) |
| maximal quotient of | D9×AGL(1,𝔽5)2, D9×#87830 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1490);