Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D61⋊#335 |
| Sylow | C61 ⋊ C2×#335 |
200 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 94 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,b^2=df,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^11,h^c=h^60,h^e=h^60536 conjugacy classes — view the full character table.
| maximal subgroup of | #30594230, #30594243, #30594287, … |
| maximal normal subgroup of | #30594230, #30594243, #30594287, … |
| maximal quotient of | #30596088, C4×#16840625, C4×#16840626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20055);