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 ⋊ #361 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=d,c^2=e,d^2=f,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×#361, C2×#14270977, #16821240, … |
| maximal normal subgroup of | D29×#361, C2×#14270977, #16821240, … |
| maximal quotient of | #16817460, #16817508, #16817539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 363);