Finite Group DatabasebetaFinite Group Databasebeta| order | 14112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C42×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| Fitting | C42×C72 ⋊ C2×C32 |
| derived, Sylow | C72 ⋊ C2×C32×C42 |
| Hall | C42×C7⋊D7 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ C2×C42 |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #127×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #104×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| maximal normal subgroup of | #127×ΓL(1,𝔽8)⋊AGL(1,𝔽7), #104×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.