Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #459×D61 |
| Fitting | C61×#459 ⋊ C2 |
| Sylow | C61 ⋊ C2×#459 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#459 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #459 | D61 |
| hypocenter | C61 | C2×#459 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
648 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1619, D61×#1622, D61×#1625, … |
| maximal normal subgroup of | D61×#1619, D61×#1622, D61×#1625, … |
| maximal quotient of | D61×#1665, D61×#1667, D61×#1669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13918);