Finite Group DatabasebetaFinite Group Databasebeta| order | 15060 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C251 · Schur multiplier (H2) = C2 |
| direct product | C5×A4×C251 |
| unambiguous semidirect product | C22⋊(C3×C5×C251) |
| unambiguous semidirect product | (C22×C5)⋊(C3×C251) |
| unambiguous semidirect product | (C22×C5×C251)⋊C3 |
| Fitting, socle, Hall | C22×C5×C251 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C5×C251 |
| Hall | C22×C251 ⋊ C3×C5 |
| Hall | C22×C5 ⋊ C3×C251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C251 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C5×C251 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C251 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C5×C251 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5020 |
5020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15060, 31);