Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D17⋊#443 |
| Fitting | C17×#135 ⋊ C4 |
| Sylow | C17 ⋊ C2×#443 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^4,e^b=eg,h^c=h^13,h^d=h^16,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17960913, #17960917, #17960932, … |
| maximal normal subgroup of | #17960913, #17960917, #17960932, … |
| maximal quotient of | D8×#63242, SD16×#63242, Q16×#63242, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21276);