Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×#125 ⋊ C4 |
| Sylow | C17 ⋊ #1989 |
260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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=f,b^2=def,c^2=eg,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^4,d^b=dg,f^b=fg,h^b=h^13,h^f=h^1694 conjugacy classes — view the full character table.
| maximal subgroup of | #17952998, #17952999, #17953000, … |
| maximal normal subgroup of | #17952998, #17952999, #17953000, … |
| maximal quotient of | #17956438, #17956439, #17956440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20690);