Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #510 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^28212 conjugacy classes — view the full character table.
| maximal subgroup of | #16821380, #16821383, #16821443, … |
| maximal normal subgroup of | #16821380, #16821383, #16821443, … |
| maximal quotient of | #16821204, #16821211, #16821281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 989);