Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C11 ⋊ Q16 |
| Sylow | C11 ⋊ #689 |
| Sylow | C5 ⋊ #4326 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 880 |
Polycyclic presentation:
2^4,5,11|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^10,c^b=cd142 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#689, #13182925, D5×#4326, … |
| maximal normal subgroup of | D11×#689, #13182925, D5×#4326, … |
| maximal quotient of | #13182419, #13182422, #13182447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 104);