Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C22×C33×C4 |
| direct product | C32×#6503⋊C3 |
| Fitting | C2×C32×C7×D4 ⋊ C2×C3 |
| Hall | #6503 ⋊ C33 |
| Hall | C32×ΓL(1,𝔽8) ⋊ #127 |
| Sylow | C7 ⋊ C33×#127 |
3024 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×#6503⋊C3, C32×#127×AGL(1,𝔽7), #72246558 |
| maximal normal subgroup of | C3⋊D3×#6503⋊C3, C32×#127×AGL(1,𝔽7), #72246558 |
Past the SmallGroups library coverage — no SmallGroups id.