Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×D4×AGL(1,𝔽7) |
| Fitting | C72×D4 ⋊ C2×C3 |
| Hall | C7×D4×D7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×D4 |
224 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 88 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, D4×D7×AGL(1,𝔽7), #72245818, … |
| maximal normal subgroup of | C7×#6548⋊C3, D4×D7×AGL(1,𝔽7), #72245818, … |
| maximal quotient of | C7×#6500⋊C3, D4×#72215772 |
Past the SmallGroups library coverage — no SmallGroups id.