Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#72245545 |
| Fitting | C23×C32×C7 ⋊ C22×C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C22×D4 |
| Sylow | C7 ⋊ C2×C3×D4×C3⋊D3 |
3264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×C3⋊D3×AGL(1,𝔽7), #72246558, #72269527 |
| maximal normal subgroup of | C2×D4×C3⋊D3×AGL(1,𝔽7), #72246558, #72269527 |
| maximal quotient of | #72246558, #72269527 |
Past the SmallGroups library coverage — no SmallGroups id.