Finite Group DatabasebetaFinite Group Databasebeta| order | 8052 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C61 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C11×C61 |
| unambiguous semidirect product | C3⋊(C22×C11×C61) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C11×C61) |
| Fitting, socle | C2×C3×C11×C61 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C11×C61 |
| Hall | C3×C11×C61 ⋊ C22 |
| Hall | C3×C61 ⋊ C22×C11 |
| Hall | C3×C11 ⋊ C22×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11×C61 | D3 |
| commutator, hypocenter | C3 | C22×C11×C61 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C11×C61 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C11×C61 | |
40 conjugacy classes of subgroups.
4026 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×D9×C61, C2×D3×C11×C61⋊C3, D32×C11×C61, … |
| maximal normal subgroup of | C2×D3×C11×C61⋊C3, C2×C3×D3×C11×C61 |
| maximal quotient of | C2×C11×D9×C61, D32×C11×C61, C2×C3×D3×C11×C61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8052, 37);