Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1799 |
380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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,b^a=bd,c^a=ce,e^a=eg,h^a=h^11,h^b=h^60,f^c=fg,h^f=h^60332 conjugacy classes — view the full character table.
| maximal subgroup of | #30594508, #30594751, #30598271, … |
| maximal normal subgroup of | #30594508, #30594751, #30598271, … |
| maximal quotient of | #30598817, #30598822, #30598825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20372);