Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #341 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^12,g^e=g^2898 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14272038, #16835185, #16835266, … |
| maximal normal subgroup of | C2×#14272038, #16835185, #16835266, … |
| maximal quotient of | #16834321, #16834323, #16834325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1424);