Finite Group DatabasebetaFinite Group Databasebeta| order | 8052 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C61 · Schur multiplier (H2) = C2 |
| direct product | D3×D11×C61 |
| unambiguous semidirect product | (D3×C11)⋊(C2×C61) |
| unambiguous semidirect product | (C3×D11)⋊(C2×C61) |
| unambiguous semidirect product | D33⋊(C2×C61) |
| Fitting, socle, Hall | C3×C11×C61 ⋊ C22 |
| derived, Hall | C3×C11 ⋊ C22×C61 |
| Hall | C11×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D3×C61 |
| Sylow | C3 ⋊ C2×D11×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D3×D11 |
| commutator, hypocenter | C3×C11 | C22×C61 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C61 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C61 | |
40 conjugacy classes of subgroups.
1281 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D11×C61, D3×D11×C61⋊C3, C3×D3×D11×C61, … |
| maximal normal subgroup of | D3×D11×C61⋊C3, C3×D3×D11×C61 |
| maximal quotient of | D9×D11×C61, C3×D3×D11×C61, D3×C61×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8052, 27);