Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#117 ⋊ C4 |
| Sylow | C17 ⋊ C2×#339 |
488 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^b=h^13,h^c=h^16,h^f=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #339×#595, #17956610, #17956627, … |
| maximal normal subgroup of | #339×#595, #17956610, #17956627, … |
| maximal quotient of | #17950370, #17950378, #17950386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20186);