Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D17⋊#436 |
| Sylow | C17 ⋊ C2×#436 |
552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=f,f^2=g,b^a=be,c^a=cg,h^a=h^4,c^b=cg,h^c=h^13,h^d=h^16,h^f=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17952013, #17952021, #17952029, … |
| maximal normal subgroup of | #17952013, #17952021, #17952029, … |
| maximal quotient of | D17⋊#1589, D17⋊#1590, D17⋊#1591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21223);