Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#41×ΓL(1,𝔽8) |
| Fitting, Hall | C72×#41 ⋊ C3 |
| Sylow | C72 ⋊ C3×#41 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245208, … |
| maximal normal subgroup of | #41×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245208, … |
Past the SmallGroups library coverage — no SmallGroups id.