Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊#1043 |
| Fitting | C22×C52×D4 ⋊ C4 |
| Sylow | C52 ⋊ D4×C22⋊C4 |
5008 conjugacy classes of subgroups.
170 conjugacy classes — view the full character table.
| maximal subgroup of | #72221206, #72223241, #72223242, … |
| maximal normal subgroup of | #72221206, #72223241, #72223242, … |
Past the SmallGroups library coverage — no SmallGroups id.