Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | ΓL(1,𝔽8)×#3752 |
| Fitting | C2×C32×C4×C7 ⋊ C2×C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C22⋊C4 |
| Sylow | C7 ⋊ C3×#3752 |
536 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×C3⋊D3×ΓL(1,𝔽8), AGL(1,𝔽7)×#3752, #72247224, … |
| maximal normal subgroup of | C22⋊C4×C3⋊D3×ΓL(1,𝔽8), AGL(1,𝔽7)×#3752, #72247224, … |
Past the SmallGroups library coverage — no SmallGroups id.