Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of AGL(1,𝔽9)⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×AGL(1,𝔽9)⋊D5 |
| Fitting, socle | C2×C32×C5 ⋊ SD16 |
| Hall | C32×C5 ⋊ C2×SD16 |
| Sylow | C32 ⋊ C2×#677 |
| Sylow | C5 ⋊ C2×AΓL(1,𝔽9) |
168 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×AΓL(1,𝔽9), C2×C3×AGL(1,𝔽9)⋊D5 |
| maximal normal subgroup of | C2×D5×AΓL(1,𝔽9), C2×C3×AGL(1,𝔽9)⋊D5 |
| maximal quotient of | C2×C3×AGL(1,𝔽9)⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5888);