Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C61 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 198 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,b^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^11,f^b=fg,d^c=dg,h^c=h^60,h^d=h^60,h^f=h^60341 conjugacy classes — view the full character table.
| maximal subgroup of | #30607734, #30607736, #30607742, … |
| maximal normal subgroup of | #30607734, #30607736, #30607742, … |
| maximal quotient of | #30609923, #30609926, #30609927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21123);