Finite Group DatabasebetaFinite Group Databasebeta| order | 6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | #444×#1043 |
| Fitting | C52×#444 ⋊ C4 |
| Sylow | C52 ⋊ C4×#444 |
4088 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #1043×AGL(1,ℤ/16), C2×#444×#1043 |
| maximal normal subgroup of | #1043×AGL(1,ℤ/16), C2×#444×#1043 |
| maximal quotient of | #1043×#1580, C2×#444×#1043 |
Past the SmallGroups library coverage — no SmallGroups id.