Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C7 |
| direct product | M16×#3862 |
| Fitting, Hall | C72×M16 ⋊ C3 |
| Sylow | C72 ⋊ C3×M16 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | M16×#64425, AGL(1,ℤ/8)×#3862, #72245254, … |
| maximal normal subgroup of | M16×#64425, AGL(1,ℤ/8)×#3862, #72245254, … |
Past the SmallGroups library coverage — no SmallGroups id.