Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#487 ⋊ C2 |
| Sylow | C17 ⋊ #3178 |
350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,c^b=cg,d^b=dg,h^b=h^16,h^c=h^16,h^d=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3178, C2×#14539459, #17904216, … |
| maximal normal subgroup of | D17×#3178, C2×#14539459, #17904216, … |
| maximal quotient of | #17034908, #17038609, #17038629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15185);