Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic55 |
| Hall | C5×C11 ⋊ C4⋊C4 |
| Sylow | C11 ⋊ C4⋊Dic5 |
| Sylow | C5 ⋊ C4⋊Dic11 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 880 |
Polycyclic presentation:
2^4,5,11|a^2=c,b^2=d,b^a=bd,e^a=e^4,f^a=f^10226 conjugacy classes — view the full character table.
| maximal subgroup of | #13182294, #13182296, #13182300, … |
| maximal normal subgroup of | #13182294, #13182296, #13182300, … |
| maximal quotient of | C4⋊(C11⋊#168), #13182428, #13182429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 99);