Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C29 ⋊ C2 |
| Sylow | C29 ⋊ #443 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^28,d^b=df,g^b=g^28476 conjugacy classes — view the full character table.
| maximal subgroup of | #16817464, #16817466, #16817467, … |
| maximal normal subgroup of | #16817464, #16817466, #16817467, … |
| maximal quotient of | C8×D232, C8×#90773, C8×Dic116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 667);