Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1855 |
278 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 72 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,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^50,d^b=dg,h^b=h^11,h^c=h^60,h^f=h^60338 conjugacy classes — view the full character table.
| maximal subgroup of | D61⋊#1855, C2×#21461773, #30615480, … |
| maximal normal subgroup of | D61⋊#1855, C2×#21461773, #30615480, … |
| maximal quotient of | #30599545, #30599548, #30599549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20464);