Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#4318⋊C5 |
| Hall | C4×#4318 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C4×M16 |
| Sylow | C11 ⋊ C4×C5×M16 |
284 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C4×M16×AGL(1,𝔽11), #72248984, #72248989, … |
| maximal normal subgroup of | C4×M16×AGL(1,𝔽11), #72248984, #72248989, … |
| maximal quotient of | #72254639 |
Past the SmallGroups library coverage — no SmallGroups id.