Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D61⋊#446 |
| Sylow | C61 ⋊ C2×#446 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Frattini | C22 | C23×#6923 |
| Fitting | C4×Q8×C61 | C4 |
| hypercenter | C4×Q8 | #6923 |
| hypocenter | C61 | C2×#446 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
400 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,c^a=cg,h^a=h^50,h^c=h^11,h^d=h^60,h^f=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | #30597706, #30597714, #30597722, … |
| maximal normal subgroup of | #30597706, #30597714, #30597722, … |
| maximal quotient of | #30614218, #30614223, C4×#16840812, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21296);