Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×D8×#1044 |
| Fitting | C2×C52×D8 ⋊ C4 |
| Sylow | C52 ⋊ C2×C4×D8 |
1570 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1570 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D8×D5⋊AGL(1,𝔽5), C2×#72220867, #72242608, … |
| maximal normal subgroup of | C2×D8×D5⋊AGL(1,𝔽5), C2×#72220867, #72242608, … |
Past the SmallGroups library coverage — no SmallGroups id.