Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D29⋊#101 |
| Sylow | C29 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^12,e^b=ef,g^c=g^28,g^e=g^2892 conjugacy classes — view the full character table.
| maximal subgroup of | #16834588, #101×#1181, #16835339, … |
| maximal normal subgroup of | #16834588, #101×#1181, #16835339, … |
| maximal quotient of | D29⋊#324, #16834735, #16834736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1534);