Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #6599⋊C8 |
| Sylow | C29 ⋊ #322 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^a=g^12,g^c=g^28152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#6599⋊C8, #16834688, C8×#90800, … |
| maximal normal subgroup of | C2×#6599⋊C8, #16834688, C8×#90800, … |
| maximal quotient of | #16834314, #6599⋊C16, #16834410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1391);