Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#72246416 |
| derived | C22⋊#997 ⋊ C22×C4 |
At least 10575 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has at least 10575 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
160 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.