Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#529 ⋊ C2 |
| Sylow | C61 ⋊ #3251 |
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^60,c^b=ceg,f^c=fg866 conjugacy classes — view the full character table.
| maximal subgroup of | #29656813, #29656819, #29656843, … |
| maximal normal subgroup of | #29656813, #29656819, #29656843, … |
| maximal quotient of | #29689941, #29689944, #29690409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 15872);