Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×ΓL(1,𝔽8)×C22⋊AGL(1,𝔽5) |
| Fitting | C23×C5×C7 ⋊ C3×C4 |
| Hall | C2×C7×C22⋊AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×C22⋊C4 |
| Hall | C5×C7 ⋊ C2×C3×C22⋊C4 |
| Sylow | C7 ⋊ C2×C3×C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C22⋊C4×ΓL(1,𝔽8) |
528 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
140 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.