Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #462 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^28,e^c=ef299 conjugacy classes — view the full character table.
| maximal subgroup of | #16818678, #16818680, #16818685, … |
| maximal normal subgroup of | #16818678, #16818680, #16818685, … |
| maximal quotient of | #16818874, #16818886, #16818896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 759);