Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D17⋊#328 |
| Fitting | C17×C22⋊Q8 ⋊ C4 |
| Sylow | C17 ⋊ C2×#328 |
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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=df,h^a=h^13,d^b=dg,e^b=efg,h^c=h^16,h^e=h^1694 conjugacy classes — view the full character table.
| maximal subgroup of | #328×#595, #17952061, #17952071, … |
| maximal normal subgroup of | #328×#595, #17952061, #17952071, … |
| maximal quotient of | #17949640, #17949647, #17949665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19879);