Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C22×#11716763 |
| Sylow | C52 ⋊ C22×#97 |
1858 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1858 conjugacy classes of subgroups — too many to draw. Only its 403 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220669, C23×#11716763, C2×#72221300, … |
| maximal normal subgroup of | C2×#72220669, C23×#11716763, C2×#72221300, … |
| maximal quotient of | C23×#11716763 |
Past the SmallGroups library coverage — no SmallGroups id.