Finite Group DatabasebetaFinite Group Databasebeta| order | 7772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D29×D67 |
| unambiguous semidirect product | (D29×C67)⋊C2 |
| unambiguous semidirect product | (C29×D67)⋊C2 |
| unambiguous semidirect product | D1943⋊C2 |
| Fitting, socle, derived, Hall | C29×C67 ⋊ C22 |
| Sylow | C67 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C67 | C22 |
| LCS | G ▷ C29×C67 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | D29×D67⋊C3, C3×D29×D67, D67×D87, … |
| maximal normal subgroup of | D29×D67⋊C3, C3×D29×D67 |
| maximal quotient of | C3×D29×D67, D67×D87, D29×D201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7772, 8);