Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| unambiguous semidirect product | D17⋊#410 |
| Fitting | C2×#41×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#410 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=g,b^a=be,e^a=eg,h^a=h^13,f^b=fg,h^d=h^16,h^f=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17956755, #17956757, #17956774, … |
| maximal normal subgroup of | #17956755, #17956757, #17956774, … |
| maximal quotient of | #17964203, #17964213, #17964217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21106);