Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | C22×#11722396 |
9194 conjugacy classes of subgroups; only the 483 normal subgroups are shown.
This group has 9194 conjugacy classes of subgroups — too many to draw. Only its 483 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#72220146, C22×#72220152 |
| maximal normal subgroup of | C22×#72220152 |
Past the SmallGroups library coverage — no SmallGroups id.