Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D17⋊#352 |
| Fitting | C17×#123 ⋊ C4 |
| Sylow | C17 ⋊ C2×#352 |
278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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=g,b^a=bd,d^a=df,f^a=fg,h^a=h^13,e^b=ef,h^c=h^16,e^d=eg,h^e=h^1682 conjugacy classes — view the full character table.
| maximal subgroup of | #352×#595, #17960822, #17961298, … |
| maximal normal subgroup of | #352×#595, #17960822, #17961298, … |
| maximal quotient of | #17958125, #17958212, #17958288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20759);