Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#72215851 |
| Fitting, Sylow | C4×#347042 ⋊ C3 |
At least 11137 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has at least 11137 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
132 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72215854, C4×#72215886 |
| maximal normal subgroup of | C4×#72215886 |
Past the SmallGroups library coverage — no SmallGroups id.