Finite Group DatabasebetaFinite Group Databasebeta| order | 6720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | D7×AGL(1,𝔽5)×SL(2,𝔽3) |
| Fitting, derived | C5×C7×Q8 ⋊ C2×C3×C4 |
| Hall | Q8×D7×AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×C7 ⋊ C2×C4×SL(2,𝔽3) |
| Sylow | C7 ⋊ C2×AGL(1,𝔽5)×SL(2,𝔽3) |
| Sylow | C5 ⋊ C4×D7×SL(2,𝔽3) |
432 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
175 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×SL(2,𝔽3)×AGL(1,𝔽7) |
| maximal normal subgroup of | AGL(1,𝔽5)×SL(2,𝔽3)×AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.