Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| unambiguous semidirect product | D61⋊#431 |
| Sylow | C61 ⋊ C2×#431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C2×C42 | #6923 |
| hypocenter | C61 | C2×#431 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ C2×C42 | |
528 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^11,h^d=h^60,h^f=h^60560 conjugacy classes — view the full character table.
| maximal subgroup of | #30596003, #30596005, #30596006, … |
| maximal normal subgroup of | #30596003, #30596005, #30596006, … |
| maximal quotient of | #30613928, C4×D61⋊(C22⋊C8), C4×D61⋊(C4⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21174);