Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #1299 |
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 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=d,b^2=e,c^2=f,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=efg,h^a=h^50,c^b=cg,h^b=h^11,h^d=h^60,h^e=h^60338 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460705, #30596995, #30597000, … |
| maximal normal subgroup of | C2×#21460705, #30596995, #30597000, … |
| maximal quotient of | #30593947, #30593959, #30593961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19396);