Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1409 |
110 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 23 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=d,b^2=g,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cfg,d^b=def,e^b=eg,h^b=h^60,d^c=dfg,e^d=eg407 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1409, C2×#21443983, #29600322, … |
| maximal normal subgroup of | D61×#1409, C2×#21443983, #29600322, … |
| maximal quotient of | #29567397, #29567429, #29567522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2674);