Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | D17⋊#568 |
| Sylow | C17 ⋊ C2×#568 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,f^2=g,d^a=dg,h^a=h^13,c^b=cg,h^e=h^16,h^f=h^16148 conjugacy classes — view the full character table.
| maximal subgroup of | #17956756, #17956761, #17956770, … |
| maximal normal subgroup of | #17956756, #17956761, #17956770, … |
| maximal quotient of | #17979415, #17979424, C4×#11763887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21502);