Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C11 ⋊ SD16 |
| Sylow | C11 ⋊ #687 |
| Sylow | C5 ⋊ #4314 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 440 |
Polycyclic presentation:
2^4,5,11|b^2=c,c^2=d,b^a=bc,c^a=cd,f^a=f^10,e^b=e^497 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4314, #13182671, #13182690, … |
| maximal normal subgroup of | D5×#4314, #13182671, #13182690, … |
| maximal quotient of | #13182294, #13182303, #13182316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 44);