Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×AGL(1,𝔽7)×PSU(3,𝔽2) |
| Fitting, socle | C2×C32×C7 ⋊ C2×C3×Q8 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C22×Q8 |
| Sylow | C7 ⋊ C22×C3×PSU(3,𝔽2) |
708 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽7)×PSU(3,𝔽2)⋊C3, C2×AGL(1,𝔽7)×AΓL(1,𝔽9) |
| maximal normal subgroup of | C2×AGL(1,𝔽7)×PSU(3,𝔽2)⋊C3, C2×AGL(1,𝔽7)×AΓL(1,𝔽9) |
Past the SmallGroups library coverage — no SmallGroups id.