Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | ΓL(1,𝔽8)×C9⋊C9 |
| Fitting | C7×C9⋊C9 ⋊ C3 |
| Sylow | C7 ⋊ C3×C9⋊C9 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×C9⋊C9, ΓL(1,𝔽8)×D9⋊C9, #72229940 |
| maximal normal subgroup of | AGL(1,𝔽7)×C9⋊C9, ΓL(1,𝔽8)×D9⋊C9, #72229940 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 159);