Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C29 ⋊ #488 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^c=g^28218 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#488, C2×#14271516, #16829811, … |
| maximal normal subgroup of | D29×#488, C2×#14271516, #16829811, … |
| maximal quotient of | #16819621, #16820166, #16820169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 902);