Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1614 |
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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=fg,b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^60,d^b=df,e^b=eg,d^c=dg683 conjugacy classes — view the full character table.
| maximal subgroup of | #29592796, #29592797, #29592808, … |
| maximal normal subgroup of | #29592796, #29592797, #29592808, … |
| maximal quotient of | #29569056, #29569111, #29569144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3535);