Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C61×#529 ⋊ C2 |
| Sylow | C61 ⋊ #3219 |
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^c=h^60866 conjugacy classes — view the full character table.
| maximal subgroup of | #29577235, #29577237, #29661375, … |
| maximal normal subgroup of | #29577235, #29577237, #29661375, … |
| maximal quotient of | #29689374, #29689761, #29690589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 15543);