Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#41×AGL(1,𝔽5) |
| Fitting | C5×C7×#41 ⋊ C4 |
| Hall | C5×C7 ⋊ C4×#41 |
| Sylow | C5 ⋊ C4×C7×#41 |
620 conjugacy classes of subgroups.
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41×AGL(1,𝔽5)×ΓL(1,𝔽8), C7×AGL(1,𝔽5)×AGL(1,ℤ/8), AGL(1,𝔽5)×#6512, … |
| maximal normal subgroup of | #41×AGL(1,𝔽5)×ΓL(1,𝔽8), C7×AGL(1,𝔽5)×AGL(1,ℤ/8), AGL(1,𝔽5)×#6512, … |
Past the SmallGroups library coverage — no SmallGroups id.