Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | ΓL(1,𝔽8)×#837 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #104 |
| Sylow | C7 ⋊ C3×#837 |
216 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×ΓL(1,𝔽8)×#104, AGL(1,𝔽7)×#837, #72254344, … |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)×#104, AGL(1,𝔽7)×#837, #72254344, … |
Past the SmallGroups library coverage — no SmallGroups id.