Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #1783 |
820 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 820 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=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^11,f^b=fg,h^f=h^60512 conjugacy classes — view the full character table.
| maximal subgroup of | #30594715, #30594731, #30594742, … |
| maximal normal subgroup of | #30594715, #30594731, #30594742, … |
| maximal quotient of | #30598115, #30598117, #30598129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20342);