Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C29 ⋊ #408 |
158 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=e,e^2=f,b^a=bd,g^a=g^12,c^b=cf,g^e=g^2898 conjugacy classes — view the full character table.
| maximal subgroup of | #16834579, #16834582, #16835337, … |
| maximal normal subgroup of | #16834579, #16834582, #16835337, … |
| maximal quotient of | #16834757, #16834759, #16834761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1522);