Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C22×D61⋊C16 |
| unambiguous semidirect product | D61⋊(C22×C16) |
| derived, Sylow | C61 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #6923 |
| commutator, hypocenter | C61 | C23×C16 |
| Frattini | C4 | C23×#6923 |
| Fitting | C22×C8×C61 | C4 |
| socle | C23×C61 | C2×C8 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C22×C8 | |
440 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#6923)⋊C16, #30606135, #30606143, … |
| maximal normal subgroup of | C2×(C2×#6923)⋊C16, #30606135, #30606143, … |
| maximal quotient of | C2×C4×D61⋊C16, C22×#16840648, C2×D61⋊(C22⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21470);