Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D61⋊AΣL(1,𝔽16) |
| Fitting | #120×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 54 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^a=bd,d^a=df,f^a=fg,h^a=h^11,e^b=ef,h^c=h^60,e^d=eg,h^e=h^60236 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×#6923, #30606516, #30606983, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×#6923, #30606516, #30606983, … |
| maximal quotient of | D61⋊#1316, D61⋊#1326, #30603973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20756);