Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C32×C4 |
| direct product | C22×#13049409 |
| derived, Sylow | C34 ⋊ C22×C42 |
6508 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 6508 conjugacy classes of subgroups — too many to draw. Only its 319 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72219698 |
| maximal normal subgroup of | C22×#72219698 |
Past the SmallGroups library coverage — no SmallGroups id.