Finite Group DatabasebetaFinite Group Databasebeta| order | 8052 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C11×D61 |
| unambiguous semidirect product | (D3×C61)⋊(C2×C11) |
| unambiguous semidirect product | (C3×D61)⋊(C2×C11) |
| unambiguous semidirect product | D183⋊(C2×C11) |
| Fitting, socle, Hall | C3×C11×C61 ⋊ C22 |
| derived, Hall | C3×C61 ⋊ C22×C11 |
| Hall | C11×C61 ⋊ C2×D3 |
| Sylow | C61 ⋊ C2×D3×C11 |
| Hall | C3×C11 ⋊ C2×D61 |
| Sylow | C3 ⋊ C2×C11×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D3×D61 |
| commutator, hypocenter | C3×C61 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C61 | C22 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
1056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D9×D61, D3×C11×D61⋊C3, C3×D3×C11×D61, … |
| maximal normal subgroup of | D3×C11×D61⋊C3, C3×D3×C11×D61 |
| maximal quotient of | C11×D9×D61, C3×D3×C11×D61, D3×C11×D183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8052, 24);