Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1317 |
150 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 36 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=d,b^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^11,d^b=de,d^c=dg,h^d=h^60506 conjugacy classes — view the full character table.
| maximal subgroup of | #30594806, #30594807, #30594824, … |
| maximal normal subgroup of | #30594806, #30594807, #30594824, … |
| maximal quotient of | #30594015, #30594023, #30594110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19436);