Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C29×#125 ⋊ C2 |
| Sylow | C29 ⋊ #490 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^28,c^b=cf,g^b=g^28,g^c=g^28212 conjugacy classes — view the full character table.
| maximal subgroup of | #16818785, #16818787, #16818790, … |
| maximal normal subgroup of | #16818785, #16818787, #16818790, … |
| maximal quotient of | #16819625, #16820188, #16820315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 915);