Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C29×M32 ⋊ C2 |
| Sylow | C29 ⋊ #360 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^28,c^b=cef,d^b=df,e^b=ef,g^b=g^28296 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#360, C2×#14270974, #16821226, … |
| maximal normal subgroup of | D29×#360, C2×#14270974, #16821226, … |
| maximal quotient of | #16817460, #16817463, #16817502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 360);