Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C24×C33 |
| direct product | C32×ΓL(1,𝔽8)×#120 |
| Fitting | C32×C7×#120 ⋊ C3 |
| Hall | C7×#120 ⋊ C33 |
| Sylow | C7 ⋊ C33×#120 |
3640 conjugacy classes of subgroups; only the 884 normal subgroups are shown.
This group has 3640 conjugacy classes of subgroups — too many to draw. Only its 884 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×ΓL(1,𝔽8)×#120, C32×#120×AGL(1,𝔽7), #120×C3⋊(C3⋊AGL(1,𝔽7)) |
| maximal normal subgroup of | C3⋊D3×ΓL(1,𝔽8)×#120, C32×#120×AGL(1,𝔽7), #120×C3⋊(C3⋊AGL(1,𝔽7)) |
Past the SmallGroups library coverage — no SmallGroups id.