Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #2231 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=df,b^2=dg,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^a=h^16,e^c=efg,f^c=fg247 conjugacy classes — view the full character table.
| maximal subgroup of | #16948715, #16948717, #16948720, … |
| maximal normal subgroup of | #16948715, #16948717, #16948720, … |
| maximal quotient of | #16950430, #16951021, #16952023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6686);