Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1803 |
308 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 125 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=d,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^60,e^c=eg,h^c=h^601238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29572082, #29572088, #29572089, … |
| maximal normal subgroup of | #29572082, #29572088, #29572089, … |
| maximal quotient of | #29572702, #29572722, #29572742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4516);