Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,𝔽5)×#1161 |
| Fitting | C5×C7×Q8 ⋊ C2×C4 |
| Hall | C5×C7 ⋊ C4×#41 |
| Sylow | C7 ⋊ #41×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#1161 |
620 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
125 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#66659, AGL(1,𝔽5)×#6477, #72218563, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#66659, AGL(1,𝔽5)×#6477, #72218563, … |
Past the SmallGroups library coverage — no SmallGroups id.