Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#13094713 |
| derived | C32×C7 ⋊ C22×C3×C4 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C22×C4 |
| Sylow | C7 ⋊ C2×C3×C4×C3⋊D3 |
776 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×C3⋊D3×AGL(1,𝔽7), C2×#72245545, C4×#13094713, … |
| maximal normal subgroup of | C2×C4×C3⋊D3×AGL(1,𝔽7), C2×#72245545, C4×#13094713, … |
| maximal quotient of | C4×#13094713, #72247206 |
Past the SmallGroups library coverage — no SmallGroups id.