Finite Group DatabasebetaFinite Group Databasebeta| order | 6852 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C571 · Schur multiplier (H2) = C2 |
| direct product | A4×C571 |
| unambiguous semidirect product | C22⋊(C3×C571) |
| Fitting, socle, Hall | C22×C571 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C571 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C571 | A4 |
| commutator, hypocenter | C22 | C3×C571 |
| Frattini | C1 | G |
| Fitting, socle | C22×C571 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C571 | |
10 conjugacy classes of subgroups.
2284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C571⋊C3, C3×A4×C571, A4×C571⋊C5, … |
| maximal normal subgroup of | A4×C571⋊C3, C3×A4×C571, A4×C571⋊C5, … |
| maximal quotient of | C22⋊C9×C571, C3×A4×C571, C5×A4×C571 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6852, 11);