Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#106×C61 ⋊ C2 |
| Sylow | C61 ⋊ #3084 |
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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=eg,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^60,d^b=dg,h^b=h^60,f^c=fg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | #29737559, #29737560, #29737571, … |
| maximal normal subgroup of | #29737559, #29737560, #29737571, … |
| maximal quotient of | #29679545, #29681019, #29681051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 14377);