Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1988 |
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=f,b^2=defg,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^60,d^b=dg,f^b=fg1238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29571927, #29571932, #29571969, … |
| maximal normal subgroup of | #29571927, #29571932, #29571969, … |
| maximal quotient of | #29579998, #29580016, #29580138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5462);