Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D61⋊#444 |
| Fitting | #135×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#444 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×#6923 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C4 | C23×#6923 |
| Fitting | #135×C61 | C4 |
| socle | C2×C61 | C2×C4×D4 |
| hypercenter | #135 | #6923 |
| hypocenter | C61 | C2×#444 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
464 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^50,e^b=eg,h^c=h^11,h^d=h^60,h^f=h^60254 conjugacy classes — view the full character table.
| maximal subgroup of | #30606641, #30606644, #30606645, … |
| maximal normal subgroup of | #30606641, #30606644, #30606645, … |
| maximal quotient of | D61⋊(SD16⋊C8), D61⋊#1579, D61⋊#1580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21281);