Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×ΓL(1,𝔽8)⋊AGL(1,𝔽5) |
| Fitting | C5×C7×Q8 ⋊ C3×C4 |
| Hall | Q8×C7⋊AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C4×Q8 |
| Hall | C5×C7 ⋊ C3×C4×Q8 |
| Hall | ΓL(1,𝔽8) ⋊ Q8×AGL(1,𝔽5) |
| Sylow | C7 ⋊ C3×Q8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ Q8×ΓL(1,𝔽8)⋊C4 |
280 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
95 conjugacy classes — view the full character table.
| maximal subgroup of | SL(2,𝔽3)×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #72218142, SD16×ΓL(1,𝔽8)⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | SL(2,𝔽3)×ΓL(1,𝔽8)⋊AGL(1,𝔽5), #72218142, SD16×ΓL(1,𝔽8)⋊AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.