Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D17⋊#446 |
| Sylow | C17 ⋊ C2×#446 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,c^a=cg,h^a=h^4,h^c=h^13,h^d=h^16,h^f=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17952017, #17952025, #17952033, … |
| maximal normal subgroup of | #17952017, #17952025, #17952033, … |
| maximal quotient of | #17968529, #17968534, C4×#11763859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21296);