Finite Group DatabasebetaFinite Group Databasebeta| order | 12096 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×AGL(1,𝔽7)×AΓL(1,𝔽9) |
| Fitting, socle | C2×C32×C7 ⋊ C2×C3×SD16 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C22×SD16 |
| Sylow | C7 ⋊ C22×C3×AΓL(1,𝔽9) |
1524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽7)×AGL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.