Finite Group DatabasebetaFinite Group Databasebeta| order | 5760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C3×C4 |
| direct product | C22⋊C4×C3⋊D3×AGL(1,𝔽5) |
| Fitting | C32×C5×C22⋊C4 ⋊ C2×C4 |
| Hall | C32×C5 ⋊ C2×C4×C22⋊C4 |
| Sylow | C32 ⋊ C2×C22⋊C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C22⋊C4×C3⋊D3 |
8160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×AGL(1,𝔽5)×#120 |
| maximal normal subgroup of | C3⋊D3×AGL(1,𝔽5)×#120 |
Past the SmallGroups library coverage — no SmallGroups id.