Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic11⋊C5 |
| unambiguous semidirect product | (Q8×Dic11)⋊C5 |
| Hall | Q8×Dic11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C4×Q8 |
| Sylow | C11 ⋊ C4×C5×Q8 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #41×Dic11⋊C5, #72248977, C4×Q8×AGL(1,𝔽11), … |
| maximal normal subgroup of | #41×Dic11⋊C5, #72248977, C4×Q8×AGL(1,𝔽11), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 352);