Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C29 ⋊ C4 |
| Sylow | C29 ⋊ #339 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^17,g^b=g^12,g^d=g^28,g^e=g^2898 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14272035, #16835174, #104×#1181, … |
| maximal normal subgroup of | C2×#14272035, #16835174, #104×#1181, … |
| maximal quotient of | #16834319, #16834325, #16834326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1421);