Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D61⋊(C4⋊C8) |
| unambiguous semidirect product | D61⋊(C2×C4⋊C8) |
| Sylow | C61 ⋊ C22×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C42 | #6923 |
| hypocenter | C61 | C22×C4⋊C8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
640 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460648, #30596088, #30596094, … |
| maximal normal subgroup of | C2×#21460648, #30596088, #30596094, … |
| maximal quotient of | C2×D61⋊#334, C2×D61⋊#335, D61⋊#1564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21143);