Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2081 |
204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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=e,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^60,c^b=cf,d^b=dg,e^b=eg,e^c=eg,f^c=fg683 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2081, C2×#21447279, #29708962, … |
| maximal normal subgroup of | D61×#2081, C2×#21447279, #29708962, … |
| maximal quotient of | #29584804, #29584814, #29584821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5970);