Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C7 |
| direct product | C2×D4×C3⋊(C7⋊D7) |
| Fitting | C2×C3×C72×D4 ⋊ C2 |
| Hall | C3×C72 ⋊ C22×D4 |
| Sylow | C72 ⋊ C2×D3×D4 |
| Sylow | C3 ⋊ C2×D4×C7⋊D7 |
2360 conjugacy classes of subgroups; only the 439 normal subgroups are shown.
This group has 2360 conjugacy classes of subgroups — too many to draw. Only its 439 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1176 |
750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×D4×C7⋊D7, C2×D4×C3⋊#64424, #72269418 |
| maximal normal subgroup of | C2×D3×D4×C7⋊D7, C2×D4×C3⋊#64424, #72269418 |
Past the SmallGroups library coverage — no SmallGroups id.