Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D17⋊#421 |
| Fitting | C2×#41×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^13,e^b=eg,h^d=h^16,h^f=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17956853, #17956855, #17956859, … |
| maximal normal subgroup of | #17956853, #17956855, #17956859, … |
| maximal quotient of | #17964696, #17964700, #17964704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21137);