Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×ΓL(1,𝔽8)×#104 |
| Fitting, Hall | C72×#104 ⋊ C3 |
| Sylow | C72 ⋊ C3×#104 |
220 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #104×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×#453, #72246295, … |
| maximal normal subgroup of | #104×ΓL(1,𝔽8)⋊D7, C7×ΓL(1,𝔽8)×#453, #72246295, … |
Past the SmallGroups library coverage — no SmallGroups id.