Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C42×C7×C3⋊D3 |
| Fitting | C32×C42×C7 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C42×C7 |
| Hall | C32×C7 ⋊ C2×C42 |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C42×D7×C3⋊D3, C7×C3⋊D3×#127, C3⋊D3×#6437, … |
| maximal normal subgroup of | C42×D7×C3⋊D3, C7×C3⋊D3×#127, C3⋊D3×#6437, … |
Past the SmallGroups library coverage — no SmallGroups id.