Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×#11716761 |
| derived, Sylow | C52 ⋊ C22×C4×C8 |
2018 conjugacy classes of subgroups; only the 483 normal subgroups are shown.
This group has 2018 conjugacy classes of subgroups — too many to draw. Only its 483 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220832, C2×#72220669, #72242644, … |
| maximal normal subgroup of | C2×#72220832, C2×#72220669, #72242644, … |
| maximal quotient of | C23×#11716761 |
Past the SmallGroups library coverage — no SmallGroups id.