Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | SD16⋊#92420 |
| Sylow | C61 ⋊ SD16⋊C8 |
176 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^11,d^b=df,h^c=h^11,h^e=h^60254 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16⋊#92420, D61⋊(SD16⋊C8), #30612297, … |
| maximal normal subgroup of | C2×SD16⋊#92420, D61⋊(SD16⋊C8), #30612297, … |
| maximal quotient of | #30597676, #30597680, #30598052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20099);