Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C17×C32 ⋊ C2 |
| Sylow | C17 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^16592 conjugacy classes — view the full character table.
| maximal subgroup of | D17×C22⋊C32, C2×#14526921, #16954516, … |
| maximal normal subgroup of | D17×C22⋊C32, C2×#14526921, #16954516, … |
| maximal quotient of | #16921662, #16921722, #16921761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2647);