Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(Dic11⋊C5) |
| unambiguous semidirect product | (C2×C4⋊Dic11)⋊C5 |
| Hall | C2×C4⋊Dic11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C4⋊C4 |
| Sylow | C11 ⋊ C2×C5×C4⋊C4 |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4⋊C4×AGL(1,𝔽11) |
| maximal normal subgroup of | C2×C4⋊C4×AGL(1,𝔽11) |
| maximal quotient of | #72269647 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 335);