Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×SD16×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1904 |
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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=df,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^11,e^b=eg,h^b=h^11,d^c=dg,e^c=eg,f^c=fg,h^f=h^60239 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21461852, D61⋊#1904, #30615761, … |
| maximal normal subgroup of | C2×#21461852, D61⋊#1904, #30615761, … |
| maximal quotient of | #30600213, #30600214, #30600223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20543);