Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C61 ⋊ C2 |
| Sylow | C61 ⋊ #3003 |
994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^60692 conjugacy classes — view the full character table.
| maximal subgroup of | #29711344, #29711347, #29711381, … |
| maximal normal subgroup of | #29711344, #29711347, #29711381, … |
| maximal quotient of | #29652381, #29652420, #29652459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13735);