Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic11⋊C5 |
| unambiguous semidirect product | (D4×Dic11)⋊C5 |
| Hall | D4×Dic11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C4×D4 |
| Sylow | C11 ⋊ C4×C5×D4 |
188 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #72248711, C4×D4×AGL(1,𝔽11), #72248717, … |
| maximal normal subgroup of | #72248711, C4×D4×AGL(1,𝔽11), #72248717, … |
| maximal quotient of | #72248711, #72248739, D4×(C11⋊C5)⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 341);