Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (Dic11⋊C4)⋊C5 |
| unambiguous semidirect product | (Dic11⋊C5)⋊C4 |
| Hall | Dic11⋊C4 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C4⋊C4 |
| Sylow | C11 ⋊ C5×C4⋊C4 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^2,5,2^2,11|a^2=e,b^2=d,b^a=be,f^a=f^10,f^c=f^958 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(C11⋊C5)⋊Q8, #66923⋊C5, #66925⋊C5, … |
| maximal normal subgroup of | C4×(C11⋊C5)⋊Q8, #66923⋊C5, #66925⋊C5, … |
| maximal quotient of | #66871⋊C5, #66872⋊C5, (Dic11⋊C5)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 15);