Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C29 ⋊ #350 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^28,c^b=cf,d^b=df308 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#350, C2×#14270947, #16821118, … |
| maximal normal subgroup of | D29×#350, C2×#14270947, #16821118, … |
| maximal quotient of | #16817418, #16817434, D4⋊#90768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 333);