Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×C29 ⋊ C4 |
| Sylow | C29 ⋊ #354 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^12,c^b=cf,d^b=def,g^b=g^28,d^c=df,g^d=g^28125 conjugacy classes — view the full character table.
| maximal subgroup of | #16834619, #16834620, #16834621, … |
| maximal normal subgroup of | #16834619, #16834620, #16834621, … |
| maximal quotient of | #16834423, #16834432, #16834473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1456);