Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D17⋊#407 |
| Sylow | C17 ⋊ C2×#407 |
1008 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,f^2=g,b^a=be,c^a=cg,h^a=h^13,h^d=h^16,h^f=h^16184 conjugacy classes — view the full character table.
| maximal subgroup of | #17950557, #17950563, #17950569, … |
| maximal normal subgroup of | #17950557, #17950563, #17950569, … |
| maximal quotient of | D17⋊#1462, D17⋊#1463, D17⋊#1464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21087);