Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #123×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2123 |
234 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 52 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,b^2=g,c^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^11,c^b=cg,e^b=ef,h^c=h^60,e^d=eg,h^e=h^60233 conjugacy classes — view the full character table.
| maximal subgroup of | #30606995, #30606996, #30606997, … |
| maximal normal subgroup of | #30606995, #30606996, #30606997, … |
| maximal quotient of | #30603828, #30603910, #30603985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20773);