Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×ΓL(1,𝔽8)×#213 |
| Fitting | C32×C7×D4 ⋊ C2×C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ D8 |
| Sylow | C7 ⋊ C32×#213 |
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 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 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#63926, C3×AGL(1,𝔽7)×#213, #72269266, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#63926, C3×AGL(1,𝔽7)×#213, #72269266, … |
Past the SmallGroups library coverage — no SmallGroups id.