Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | #121×#1044 |
| Fitting | C52×#121 ⋊ C4 |
| Sylow | C52 ⋊ C4×#121 |
2074 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #121×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | #121×D5⋊AGL(1,𝔽5) |
| maximal quotient of | #72242608 |
Past the SmallGroups library coverage — no SmallGroups id.