Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of ΓL(1,𝔽16)⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×ΓL(1,𝔽16)⋊D3 |
| Fitting | C32×C4×C5 ⋊ C2×C4 |
| derived, Hall | C32×C5 ⋊ C2×C42 |
| Sylow | C32 ⋊ C2×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#624 |
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72230187, #72230254, C4×D32×AGL(1,𝔽5), … |
| maximal normal subgroup of | #72230187, #72230254, C4×D32×AGL(1,𝔽5), … |
| maximal quotient of | AGL(1,𝔽5)×ΓL(1,𝔽16)⋊D3, #72254811, #72260236 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5048);