Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#72220245 |
| Sylow | C34 ⋊ C2×#106 |
1121 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 1121 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72252820 |
| maximal normal subgroup of | #72252820 |
Past the SmallGroups library coverage — no SmallGroups id.