Finite Group DatabasebetaFinite Group Databasebeta| order | 6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #360×#1043 |
| Fitting | C52×#360 ⋊ C4 |
| Sylow | C52 ⋊ C4×#360 |
1864 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #1043×AGL(1,ℤ/16), C2×#360×#1043 |
| maximal normal subgroup of | #1043×AGL(1,ℤ/16), C2×#360×#1043 |
| maximal quotient of | #1043×#1333, C2×#360×#1043 |
Past the SmallGroups library coverage — no SmallGroups id.