Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#13103866 |
| Sylow | C52 ⋊ C2×#405 |
1330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220832, #72242621, #72242643, … |
| maximal normal subgroup of | C2×#72220832, #72242621, #72242643, … |
Past the SmallGroups library coverage — no SmallGroups id.