Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D3×D4×AGL(1,ℤ/8) |
| Fitting | C3×D4×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ C2×D4×AGL(1,ℤ/8) |
25424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10576108, D3×S4×AGL(1,ℤ/8) |
| maximal normal subgroup of | D3×#10576108 |
| automorphism group of | #4896, #4897, #5142, … |
Past the SmallGroups library coverage — no SmallGroups id.