Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C5 |
| direct product | C5⋊D5×#347 |
| Fitting | C52×#347 ⋊ C2 |
| Sylow | C52 ⋊ C2×#347 |
672 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×#1043, C5⋊D5×AGL(1,ℤ/16), #72253139, … |
| maximal normal subgroup of | #347×#1043, C5⋊D5×AGL(1,ℤ/16), #72253139, … |
| maximal quotient of | C5⋊D5×#1313, C2×C5⋊D5×#347 |
Past the SmallGroups library coverage — no SmallGroups id.