Finite Group DatabasebetaFinite Group Databasebeta| order | 7772 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | C2×C29×D67 |
| unambiguous semidirect product | C67⋊(C22×C29) |
| unambiguous semidirect product | (C2×C67)⋊(C2×C29) |
| Fitting, socle | C2×C29×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C22×C29 |
| Hall | C29×C67 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D67 |
| commutator, hypocenter | C67 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C29 | |
20 conjugacy classes of subgroups.
2030 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29×D67⋊C3, D3×C29×D67, C2×C3×C29×D67, … |
| maximal normal subgroup of | C2×C29×D67⋊C3, C2×C3×C29×D67 |
| maximal quotient of | D3×C29×D67, C2×C3×C29×D67, C2×C29×D201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7772, 11);