Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C29 ⋊ #543 |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^c=g^28302 conjugacy classes — view the full character table.
| maximal subgroup of | #16818414, #16818417, #16818448, … |
| maximal normal subgroup of | #16818414, #16818417, #16818448, … |
| maximal quotient of | #16822104, #16822106, #16822220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1175);