Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C29×M32 ⋊ C2 |
| Sylow | C29 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^28,d^b=de,e^b=ef,g^b=g^28296 conjugacy classes — view the full character table.
| maximal subgroup of | #16821389, #16821392, #16821439, … |
| maximal normal subgroup of | #16821389, #16821392, #16821439, … |
| maximal quotient of | #16821205, #16821209, #16821280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 987);