Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C29 ⋊ #501 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,c^b=cf,g^b=g^28212 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#501, C2×#14271570, #16830013, … |
| maximal normal subgroup of | D29×#501, C2×#14271570, #16830013, … |
| maximal quotient of | #16819657, #16820228, #16820229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 956);