Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #3094 |
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | #29577080, #29577086, #29577206, … |
| maximal normal subgroup of | #29577080, #29577086, #29577206, … |
| maximal quotient of | #29679820, #29680759, #29681263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 14446);