Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C4 · Schur multiplier (H2) = C22×C33 |
| direct product | C32×(C2×AGL(1,𝔽7))⋊C4 |
| Fitting | C2×C32×C4×C7 ⋊ C2×C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C22⋊C4 |
| Hall | (C2×D7)⋊C4 ⋊ C33 |
| Sylow | C7 ⋊ C33×C22⋊C4 |
952 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 344 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C22⋊C4×AGL(1,𝔽7), C3⋊D3×(C2×AGL(1,𝔽7))⋊C4, #72247224, … |
| maximal normal subgroup of | C32×C22⋊C4×AGL(1,𝔽7), C3⋊D3×(C2×AGL(1,𝔽7))⋊C4, #72247224, … |
Past the SmallGroups library coverage — no SmallGroups id.