Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q16×C29 ⋊ C2 |
| Sylow | C29 ⋊ #473 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,e^c=ef,g^c=g^28212 conjugacy classes — view the full character table.
| maximal subgroup of | #16821460, #16821462, #16821467, … |
| maximal normal subgroup of | #16821460, #16821462, #16821467, … |
| maximal quotient of | #16818854, #16818859, #16818878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 821);