Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×ΓL(1,𝔽8)×#120 |
| Fitting, Hall | C72×#120 ⋊ C3 |
| Sylow | C72 ⋊ C3×#120 |
650 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #120×ΓL(1,𝔽8)⋊D7, ΓL(1,𝔽8)2×#120, C7×#89804⋊C3, … |
| maximal normal subgroup of | #120×ΓL(1,𝔽8)⋊D7, ΓL(1,𝔽8)2×#120, C7×#89804⋊C3, … |
| maximal quotient of | C7×ΓL(1,𝔽8)×B(4,𝔽2), C7×ΓL(1,𝔽8)×#453 |
Past the SmallGroups library coverage — no SmallGroups id.