Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#6474⋊C3 |
| Fitting | C5×C7×D8 ⋊ C2×C3 |
| Hall | C5×#6474 ⋊ C3 |
| Hall | #6474 ⋊ C3×C5 |
| Hall | C5×ΓL(1,𝔽8) ⋊ AGL(1,ℤ/8) |
| Hall | C5×C7 ⋊ C3×AGL(1,ℤ/8) |
| Hall | ΓL(1,𝔽8) ⋊ C5×AGL(1,ℤ/8) |
| Sylow | C7 ⋊ C3×C5×AGL(1,ℤ/8) |
272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
200 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#6474⋊C3, C5×AGL(1,ℤ/8)×AGL(1,𝔽7), #72218479 |
| maximal normal subgroup of | D5×#6474⋊C3, C5×AGL(1,ℤ/8)×AGL(1,𝔽7), #72218479 |
Past the SmallGroups library coverage — no SmallGroups id.