Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#6408⋊C3 |
| Hall | C7×#6408 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ #99 |
| Sylow | C72 ⋊ C3×#99 |
235 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
301 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72246120, C7×#89804⋊C3, #72246127 |
| maximal normal subgroup of | #72246120, C7×#89804⋊C3, #72246127 |
Past the SmallGroups library coverage — no SmallGroups id.