Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#6495⋊C3 |
| Fitting | C2×C72×D4 ⋊ C2×C3 |
| Hall | C7×#6495 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ AGL(1,ℤ/8) |
| Sylow | C72 ⋊ C3×AGL(1,ℤ/8) |
299 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #72245056, ΓL(1,𝔽8)×#6495⋊C3, C7×#89849⋊C3, … |
| maximal normal subgroup of | #72245056, ΓL(1,𝔽8)×#6495⋊C3, C7×#89849⋊C3, … |
Past the SmallGroups library coverage — no SmallGroups id.