Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C3⋊D3×(C22⋊Dic7)⋊C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×C22⋊C4 |
| Sylow | C7 ⋊ C3×C22⋊C4×C3⋊D3 |
1856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽7), C3⋊D3×#6500⋊C3, C3⋊D3×#10620789 |
| maximal normal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽7), C3⋊D3×#6500⋊C3, C3⋊D3×#10620789 |
Past the SmallGroups library coverage — no SmallGroups id.