Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×M16×ΓL(1,𝔽8) |
| Fitting, Hall | C72×M16 ⋊ C3 |
| Sylow | C72 ⋊ C3×M16 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245203, … |
| maximal normal subgroup of | M16×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×AGL(1,ℤ/8), #72245203, … |
Past the SmallGroups library coverage — no SmallGroups id.