Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C2 |
| direct product | #126×AGL(1,𝔽8) |
| unambiguous semidirect product | (C23×#126)⋊C7 |
| Fitting, Sylow | C23×#126 ⋊ C7 |
789 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 789 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083524);