Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #473 |
100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^28,e^c=ef170 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#473, C2×#14271436, #16829207, … |
| maximal normal subgroup of | D29×#473, C2×#14271436, #16829207, … |
| maximal quotient of | #16818855, #16818860, #16818879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 822);