Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×SD16×#1043 |
| Fitting | C2×C52×SD16 ⋊ C4 |
| Sylow | C52 ⋊ C2×C4×SD16 |
2208 conjugacy classes of subgroups.
140 conjugacy classes — view the full character table.
| maximal subgroup of | #492×#1043, C2×AGL(1,ℤ/8)×#1043, #496×#1043, … |
| maximal normal subgroup of | #492×#1043, C2×AGL(1,ℤ/8)×#1043, #496×#1043, … |
| maximal quotient of | #492×#1043, #498×#1043, #486×#1043, … |
Past the SmallGroups library coverage — no SmallGroups id.