Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1865 |
298 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 113 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=fg,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^60,d^b=dg,e^b=eg,d^c=dg,e^c=eg1238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#1865, C2×#21446087, #29680956, … |
| maximal normal subgroup of | D61×#1865, C2×#21446087, #29680956, … |
| maximal quotient of | #29573945, #29573973, #29574096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4778);