Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊#3633 |
| Fitting | SD16×C17 ⋊ C8 |
| Sylow | C17 ⋊ SD16⋊C8 |
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^7,17|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^8,d^b=df,h^c=h^9,h^e=h^13,h^g=h^1658 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16⋊#3633, #17982866, AGL(1,ℤ/8)×#3633, … |
| maximal normal subgroup of | C2×SD16⋊#3633, #17982866, AGL(1,ℤ/8)×#3633, … |
| maximal quotient of | #17981619, #17981620, #17981635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21639);