Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #124×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1885 |
360 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 68 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,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^50,d^b=dg,e^b=eg,f^b=fg,h^b=h^11,d^c=dg,f^c=fg,h^f=h^60242 conjugacy classes — view the full character table.
| maximal subgroup of | #30595149, #30595152, #30595181, … |
| maximal normal subgroup of | #30595149, #30595152, #30595181, … |
| maximal quotient of | #30599885, #30599886, #30599887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20515);