Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1485 |
218 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 62 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=f,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^11,c^b=cfg,d^b=df,h^e=h^60248 conjugacy classes — view the full character table.
| maximal subgroup of | #30598615, #30598616, #30598617, … |
| maximal normal subgroup of | #30598615, #30598616, #30598617, … |
| maximal quotient of | #30595737, #30595739, #30595756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19832);