Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×C4⋊ΓL(1,𝔽16) |
| Fitting | C32×C4×C5 ⋊ C2×C4 |
| Hall | C32×C5 ⋊ C2×C4⋊C4 |
| Sylow | C32 ⋊ C2×C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ D3×C4⋊Dic3 |
394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×ΓL(1,𝔽16), #72230100, D3×AGL(1,𝔽5)×D12, … |
| maximal normal subgroup of | D3×D4×ΓL(1,𝔽16), #72230100, D3×AGL(1,𝔽5)×D12, … |
| maximal quotient of | #72269797 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5022);