Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C4×C3⋊D3×Dic7 |
| derived, Hall | C32×C7 ⋊ C2×C42 |
| Sylow | C32 ⋊ C2×C4×Dic7 |
| Sylow | C7 ⋊ C42×C3⋊D3 |
648 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 196 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1008 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C42×D7×C3⋊D3, C3⋊D3×#6503, C4×C3⋊D3×ΓL(1,𝔽8)⋊C4, … |
| maximal normal subgroup of | C42×D7×C3⋊D3, C3⋊D3×#6503, C4×C3⋊D3×ΓL(1,𝔽8)⋊C4, … |
Past the SmallGroups library coverage — no SmallGroups id.