Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#124×C61 ⋊ C2 |
| Sylow | C61 ⋊ #3040 |
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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=dg,f^a=fg,f^c=fg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | #29577087, #29577093, #29577094, … |
| maximal normal subgroup of | #29577087, #29577093, #29577094, … |
| maximal quotient of | #29663963, #29663972, #29663981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 14000);