Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1594 |
176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^60,c^b=cg,d^b=df,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | #29591972, #29591974, #29591986, … |
| maximal normal subgroup of | #29591972, #29591974, #29591986, … |
| maximal quotient of | #29570848, #29571274, #29573968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3424);