Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2069 |
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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=de,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,f^b=fg,h^b=h^60,d^c=dg683 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2069, C2×#21447217, #29708736, … |
| maximal normal subgroup of | D61×#2069, C2×#21447217, #29708736, … |
| maximal quotient of | #29584638, #29584640, #29584642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5908);