Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1857 |
272 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,e^b=eg,h^b=h^60,d^c=dg872 conjugacy classes — view the full character table.
| maximal subgroup of | #29567441, #29567443, #29596837, … |
| maximal normal subgroup of | #29567441, #29567443, #29596837, … |
| maximal quotient of | #29573879, #29573889, #29573998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4724);