Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C5⋊D5×#509 |
| Fitting | C52×#509 ⋊ C2 |
| Sylow | C52 ⋊ C2×#509 |
1600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #509×#1043, C5⋊D5×AGL(1,ℤ/16), #72253164, … |
| maximal normal subgroup of | #509×#1043, C5⋊D5×AGL(1,ℤ/16), #72253164, … |
| maximal quotient of | C5⋊D5×#2177, C2×C5⋊D5×#509 |
Past the SmallGroups library coverage — no SmallGroups id.