Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D29⋊M32 |
| Sylow | C29 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^12,g^c=g^28,g^d=g^28152 conjugacy classes — view the full character table.
| maximal subgroup of | #16834535, #16834538, #16834541, … |
| maximal normal subgroup of | #16834535, #16834538, #16834541, … |
| maximal quotient of | #16835693, #16835698, #16835699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1605);