Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D8×ΓL(1,𝔽8) |
| Fitting, Hall | C72×D8 ⋊ C3 |
| Sylow | C72 ⋊ C3×D8 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | D8×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245205, … |
| maximal normal subgroup of | D8×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245205, … |
Past the SmallGroups library coverage — no SmallGroups id.