Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C4×(C3⋊D3)⋊(C22⋊A4) |
| Fitting | C24×C32×C4 ⋊ C2×C3 |
| derived | C24×C32 ⋊ C2×C3×C4 |
10874 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 10874 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72213266 |
| maximal normal subgroup of | C4×#72213266 |
Past the SmallGroups library coverage — no SmallGroups id.