Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D61⋊#361 |
| Sylow | C61 ⋊ C2×#361 |
256 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 64 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,d^2=f,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^11,d^b=dfg,e^b=eg,f^b=fg,h^c=h^60,h^e=h^60242 conjugacy classes — view the full character table.
| maximal subgroup of | #361×#6923, #30606623, #30606969, … |
| maximal normal subgroup of | #361×#6923, #30606623, #30606969, … |
| maximal quotient of | D61⋊#1333, #30604426, #30604428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20834);