Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #2143 |
220 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 220 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,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^11,c^b=cg,d^b=df,f^b=fg,h^b=h^60,h^c=h^60,h^e=h^60242 conjugacy classes — view the full character table.
| maximal subgroup of | #30606632, #30606646, #30606970, … |
| maximal normal subgroup of | #30606632, #30606646, #30606970, … |
| maximal quotient of | #30604405, #30604408, #30604409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20826);