Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#1159⋊C3 |
| Fitting | C72×D4 ⋊ C2×C3 |
| Hall | C7×#1159 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ #41 |
| Sylow | C72 ⋊ C3×#41 |
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#6548⋊C3, #72245794, #72245804, … |
| maximal normal subgroup of | C7×#6548⋊C3, #72245794, #72245804, … |
Past the SmallGroups library coverage — no SmallGroups id.