Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C22×#13049804 |
| Fitting, socle | C22×C34 ⋊ SD16 |
| Sylow | C34 ⋊ C22×SD16 |
2161 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 2161 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72219722, C22×#72210346 |
| maximal normal subgroup of | C2×#72219722, C22×#72210346 |
Past the SmallGroups library coverage — no SmallGroups id.