Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1314 |
140 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 40 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,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^11,d^b=de,h^b=h^60,h^d=h^60524 conjugacy classes — view the full character table.
| maximal subgroup of | #30594057, #30594058, #30594059, … |
| maximal normal subgroup of | #30594057, #30594058, #30594059, … |
| maximal quotient of | #30594014, #30594016, #30594018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19431);