Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C29×#99 ⋊ C2 |
| Sylow | C29 ⋊ #458 |
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=f,b^a=bd,c^a=ce,g^a=g^28,e^b=ef,d^c=df,g^c=g^28170 conjugacy classes — view the full character table.
| maximal subgroup of | #16821484, #16821485, #16821489, … |
| maximal normal subgroup of | #16821484, #16821485, #16821489, … |
| maximal quotient of | #16818479, #16818480, #16818484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 740);