Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C29×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C29 ⋊ #576 |
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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|e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^28,d^c=df,g^d=g^28176 conjugacy classes — view the full character table.
| maximal subgroup of | #16831253, #16831255, #16831257, … |
| maximal normal subgroup of | #16831253, #16831255, #16831257, … |
| maximal quotient of | #16828016, #16828017, #16828091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1353);