Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13×C23 · Schur multiplier (H2) = C2 |
| direct product | C13×C23×C22⋊C9 |
| unambiguous semidirect product | C22⋊(C9×C13×C23) |
| unambiguous semidirect product | (C22×C23)⋊(C9×C13) |
| derived, Sylow | C22 ⋊ C9×C13×C23 |
| Hall | C22×C13×C23 ⋊ C9 |
| Hall | C22×C23 ⋊ C9×C13 |
| Hall | C22×C13 ⋊ C9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13×C23 | A4 |
| commutator, hypocenter | C22 | C9×C13×C23 |
| Frattini | C3 | A4×C13×C23 |
| Fitting, socle, prime radical | C22×C3×C13×C23 | C3 |
| cosocle | C22×C3 | C3×C13×C23 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C13×C23 | |
32 conjugacy classes of subgroups.
3588 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 32);