Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D61⋊#504 |
| Sylow | C61 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22×#6923 |
| commutator, socle | C2×C61 | C23×C8 |
| Frattini | C4 | C23×#6923 |
| Fitting | #131×C61 | C4 |
| hypercenter | #131 | #6923 |
| hypocenter | C61 | C2×#504 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ #131 | |
368 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 200 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,e^2=f,f^2=g,h^a=h^11,c^b=cg,h^d=h^60,h^e=h^60380 conjugacy classes — view the full character table.
| maximal subgroup of | #30606467, #30606473, #30607657, … |
| maximal normal subgroup of | #30606467, #30606473, #30607657, … |
| maximal quotient of | #30623818, #30623830, #30623831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21475);