Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#4246⋊C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×C32×#67 |
904 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222042, C2×C3×#67×AGL(1,𝔽7), C2×#72222040 |
| maximal normal subgroup of | C2×#72222042, C2×C3×#67×AGL(1,𝔽7), C2×#72222040 |
| maximal quotient of | C3×#72245537 |
Past the SmallGroups library coverage — no SmallGroups id.