Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×C22⋊C4×ΓL(1,𝔽8) |
| Fitting | C5×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | C7×D5×C22⋊C4 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×C22⋊C4 |
| Hall | C5×C7 ⋊ C2×C3×C22⋊C4 |
| Sylow | C7 ⋊ C3×D5×C22⋊C4 |
| Sylow | C5 ⋊ C2×C22⋊C4×ΓL(1,𝔽8) |
528 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 147 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×C22⋊C4×AGL(1,𝔽7), C22⋊C4×AGL(1,𝔽5)×ΓL(1,𝔽8), C22⋊C4×ΓL(1,𝔽8)⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | D5×C22⋊C4×AGL(1,𝔽7), C22⋊C4×AGL(1,𝔽5)×ΓL(1,𝔽8), C22⋊C4×ΓL(1,𝔽8)⋊AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.