Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#90770 |
| Sylow | C29 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=c,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 | D4⋊#90770, #16834443, #16834444, … |
| maximal normal subgroup of | D4⋊#90770, #16834443, #16834444, … |
| maximal quotient of | #16834514, #16834521, #16834530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1469);