Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1319 |
134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,h^b=h^60,d^c=dg686 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1319, C2×#21443752, #29589116, … |
| maximal normal subgroup of | D61×#1319, C2×#21443752, #29589116, … |
| maximal quotient of | #29566637, #29566645, #29566760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2443);