Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C22⋊C4×C3⋊(C3⋊AGL(1,𝔽7)) |
| Fitting | C32×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×C22⋊C4 |
| Sylow | C7 ⋊ C3×C22⋊C4×C3⋊D3 |
1856 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 1856 conjugacy classes of subgroups — too many to draw. Only its 252 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽7), #120×C3⋊(C3⋊AGL(1,𝔽7)) |
| maximal normal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽7), #120×C3⋊(C3⋊AGL(1,𝔽7)) |
Past the SmallGroups library coverage — no SmallGroups id.