Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | D7×#1792 |
| Fitting | C7×#1792 ⋊ C2 |
| Sylow | C7 ⋊ C2×#1792 |
4114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#1792, D7×#13343 |
| maximal normal subgroup of | AGL(1,𝔽7)×#1792, D7×#13343 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 168849);