Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C32 |
| direct product | C22×#13049783 |
| Fitting, socle | C22×C34 ⋊ C4⋊C4 |
| Sylow | C34 ⋊ C22×C4⋊C4 |
2214 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 2214 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213277 |
| maximal normal subgroup of | C22×#72213277 |
Past the SmallGroups library coverage — no SmallGroups id.