Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C29×C4⋊C8 ⋊ C2 |
| Sylow | C29 ⋊ #474 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=d,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^28,e^c=ef,g^c=g^28299 conjugacy classes — view the full character table.
| maximal subgroup of | #16818672, #16818673, #16818686, … |
| maximal normal subgroup of | #16818672, #16818673, #16818686, … |
| maximal quotient of | #16819493, #16819742, #16820064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 830);