Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C172 · Schur multiplier (H2) = C2×C17 |
| direct product | C172×C22⋊C9 |
| unambiguous semidirect product | C22⋊(C9×C172) |
| unambiguous semidirect product | (C22×C17)⋊(C9×C17) |
| derived, Sylow | C22 ⋊ C9×C172 |
| Hall | C22×C172 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C172 | A4 |
| commutator, hypocenter | C22 | C9×C172 |
| Frattini | C3 | A4×C172 |
| Fitting, socle, prime radical | C22×C3×C172 | C3 |
| cosocle | C22×C3 | C3×C172 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C172 | |
160 conjugacy classes of subgroups.
3468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 66);