Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C22 |
| direct product | C3×C7×#932 |
| Fitting | C2×C32×C7×D4 ⋊ C2 |
| Hall | C32×C7 ⋊ AGL(1,ℤ/8) |
| Sylow | C32 ⋊ C7×AGL(1,ℤ/8) |
326 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
441 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#10595100, C3×D7×#932, #72245926, … |
| maximal normal subgroup of | C7×#10595100, C3×D7×#932, #72245926, … |
Past the SmallGroups library coverage — no SmallGroups id.