Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C32 |
| direct product | C22×#13049818 |
| Fitting, socle | C22×C34 ⋊ C2×Q8 |
| Sylow | C34 ⋊ C23×Q8 |
2998 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 2998 conjugacy classes of subgroups — too many to draw. Only its 462 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 | C22×#72210346, #72220785, #72220850, … |
| maximal normal subgroup of | C22×#72210346, #72220785, #72220850, … |
Past the SmallGroups library coverage — no SmallGroups id.