Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33×C4 · Schur multiplier (H2) = C24×C33 |
| direct product | C32×C22⋊C4×AGL(1,𝔽7) |
| Fitting | C32×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | D7×C22⋊C4 ⋊ C33 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×C22⋊C4 |
| Sylow | C7 ⋊ C2×C33×C22⋊C4 |
3696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽7), C32×#120×AGL(1,𝔽7) |
| maximal normal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽7), C32×#120×AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.