Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×C4⋊#64424 |
| Fitting | C22×C4×C72 ⋊ C2×C3 |
| Hall | C22×C4⋊(C7⋊D7) ⋊ C3 |
| Hall | #3861 ⋊ C22×D4 |
| Sylow | C72 ⋊ C22×C3×D4 |
2360 conjugacy classes of subgroups; only the 399 normal subgroups are shown.
This group has 2360 conjugacy classes of subgroups — too many to draw. Only its 399 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D4×#64424, C2×D3×C4⋊#64424, C2×#72245153, … |
| maximal normal subgroup of | C22×D4×#64424, C2×#72245153, C2×#72214277, … |
| maximal quotient of | C2×D3×C4⋊#64424, C2×#72245153 |
Past the SmallGroups library coverage — no SmallGroups id.