Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#90770 |
| Sylow | C29 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^12,g^d=g^28152 conjugacy classes — view the full character table.
| maximal subgroup of | #16834412, #16834413, #16834414, … |
| maximal normal subgroup of | #16834412, #16834413, #16834414, … |
| maximal quotient of | #16834412, #16834428, D4⋊#90770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1443);