Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#13104727 |
| Sylow | C52 ⋊ C22×M32 |
1600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×M32×#1043, C2×#72242137, C2×#72242145, … |
| maximal normal subgroup of | C2×M32×#1043, C2×#72242137, C2×#72242145, … |
Past the SmallGroups library coverage — no SmallGroups id.