Finite Group DatabasebetaFinite Group Databasebeta| order | 6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×M32×#1043 |
| Fitting | C2×C52×M32 ⋊ C4 |
| Sylow | C52 ⋊ C2×C4×M32 |
3672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#347×#1043, C2×#365×#1043, C2×#509×#1043, … |
| maximal normal subgroup of | C2×#347×#1043, C2×#365×#1043, C2×#509×#1043, … |
Past the SmallGroups library coverage — no SmallGroups id.