Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #324 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^12,d^b=de,g^d=g^28134 conjugacy classes — view the full character table.
| maximal subgroup of | #16834420, #16834421, #16834422, … |
| maximal normal subgroup of | #16834420, #16834421, #16834422, … |
| maximal quotient of | #16834310, #16834330, #16834428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1394);