Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C7 |
| direct product | C2×C4×D3×C7⋊D7 |
| Fitting | C2×C3×C4×C72 ⋊ C22 |
| derived, Hall | C3×C72 ⋊ C23×C4 |
| Sylow | C72 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C22×C4×C7⋊D7 |
2360 conjugacy classes of subgroups; only the 460 normal subgroups are shown.
This group has 2360 conjugacy classes of subgroups — too many to draw. Only its 460 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1176 |
624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×D4×C7⋊D7, C2×C4×D3×#64424, D3×#13096284, … |
| maximal normal subgroup of | C2×D3×D4×C7⋊D7, C2×C4×D3×#64424, D3×#13096284, … |
Past the SmallGroups library coverage — no SmallGroups id.