Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#72215837 |
| Fitting | C4×#62817 ⋊ D3 |
| derived | C22⋊(C22⋊A4) ⋊ C23×C4 |
53031 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 53031 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72215845, C4×#72215886 |
| maximal normal subgroup of | C4×#72215845, C4×#72215886 |
Past the SmallGroups library coverage — no SmallGroups id.