Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | ΓL(1,𝔽8)×(C2×D7)⋊C4 |
| Fitting | C2×C4×C72 ⋊ C2×C3 |
| Hall | C7×(C2×D7)⋊C4 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C22⋊C4 |
| Sylow | C72 ⋊ C3×C22⋊C4 |
144 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #72245767, #72245905, ΓL(1,𝔽8)×#6500 |
| maximal normal subgroup of | #72245767, #72245905, ΓL(1,𝔽8)×#6500 |
| maximal quotient of | ΓL(1,𝔽8)×#6379, ΓL(1,𝔽8)×#6380 |
Past the SmallGroups library coverage — no SmallGroups id.