Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C24×C33 |
| direct product | C32×#6445⋊C3 |
| Fitting | C32×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | #6445 ⋊ C33 |
| Hall | C32×ΓL(1,𝔽8) ⋊ #120 |
| Sylow | C7 ⋊ C33×#120 |
3640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×#6445⋊C3, C32×#120×AGL(1,𝔽7) |
| maximal normal subgroup of | C3⋊D3×#6445⋊C3, C32×#120×AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.