Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C5 |
| direct product | C5⋊D5×#365 |
| Fitting | C52×#365 ⋊ C2 |
| Sylow | C52 ⋊ C2×#365 |
608 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #365×#1043, C5⋊D5×AGL(1,ℤ/16), #72253129, … |
| maximal normal subgroup of | #365×#1043, C5⋊D5×AGL(1,ℤ/16), #72253129, … |
| maximal quotient of | C5⋊D5×#1368, C2×C5⋊D5×#365 |
Past the SmallGroups library coverage — no SmallGroups id.