Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4314⋊C5 |
| Fitting | C8×C11 ⋊ C2×C5 |
| Hall | #4314 ⋊ C5 |
| Hall | C11⋊C5 ⋊ SD16 |
| Sylow | C11 ⋊ C5×SD16 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^2,5,2^2,11|b^2=d,d^2=e,b^a=bd,d^a=de,f^a=f^10,f^c=f^943 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#4314⋊C5, #66957⋊C5, #66961⋊C5, … |
| maximal normal subgroup of | C2×#4314⋊C5, #66957⋊C5, #66961⋊C5, … |
| maximal quotient of | #66881⋊C5, #66885⋊C5, #66880⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 9);