Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D7×#1891 |
| Fitting | C7×#1891 ⋊ C2 |
| Sylow | C7 ⋊ C2×#1891 |
1870 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#23882, AGL(1,𝔽7)×#1891 |
| maximal normal subgroup of | D7×#23882, AGL(1,𝔽7)×#1891 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 171215);