Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52×C49 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×A4×C49 |
| unambiguous semidirect product | C22⋊(C3×C52×C49) |
| unambiguous semidirect product | (C22×C5)⋊(C3×C5×C49) |
| Fitting, Hall | C22×C52×C49 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C52×C49 |
| Hall | C22×C49 ⋊ C3×C52 |
| Hall | C22×C52 ⋊ C3×C49 |
120 conjugacy classes of subgroups.
4900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 184);