Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C23×C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2120 |
264 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 264 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,c^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^11,e^b=ef,e^d=eg,h^e=h^60506 conjugacy classes — view the full character table.
| maximal subgroup of | #30606517, #30606521, #30606523, … |
| maximal normal subgroup of | #30606517, #30606521, #30606523, … |
| maximal quotient of | #30603816, #30603905, #30603972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20761);