Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C29 ⋊ #451 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^28,d^b=df,g^b=g^28299 conjugacy classes — view the full character table.
| maximal subgroup of | #16818450, #16818451, #16818456, … |
| maximal normal subgroup of | #16818450, #16818451, #16818456, … |
| maximal quotient of | #16818451, #16818468, #16818519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 707);