Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×#11716761 |
| derived, Sylow | C52 ⋊ C42×C8 |
1074 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
224 conjugacy classes — view the full character table.
| maximal subgroup of | #72223458, #72226594, #72226595, … |
| maximal normal subgroup of | #72223458, #72226594, #72226595, … |
| maximal quotient of | #72242167 |
Past the SmallGroups library coverage — no SmallGroups id.