Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#1142⋊C3 |
| Hall | C7×#1142 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ SD16 |
| Sylow | C72 ⋊ C3×SD16 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | #72245024, C7×#6495⋊C3, #72245036, … |
| maximal normal subgroup of | #72245024, C7×#6495⋊C3, #72245036, … |
Past the SmallGroups library coverage — no SmallGroups id.