Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D29⋊(C4⋊C8) |
| Sylow | C29 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^12,g^c=g^28,g^e=g^28152 conjugacy classes — view the full character table.
| maximal subgroup of | #16834321, #16834327, #16834356, … |
| maximal normal subgroup of | #16834321, #16834327, #16834356, … |
| maximal quotient of | D29⋊#334, D29⋊#335, #16835040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1550);