Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#63241 |
| Sylow | C17 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^9,c^b=ce,h^d=h^13,h^f=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#63241, #17982085, #17982087, … |
| maximal normal subgroup of | C2×Q8⋊#63241, #17982085, #17982087, … |
| maximal quotient of | #17981167, #17981181, #17981253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21564);