Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C5 · Schur multiplier (H2) = C2×C36 |
| direct product | C33×C5×A4 |
| unambiguous semidirect product | C22⋊(C34×C5) |
| unambiguous semidirect product | (C22×C3)⋊(C33×C5) |
| unambiguous semidirect product | (C22×C5)⋊C34 |
| unambiguous semidirect product | (C22×C3×C5)⋊C33 |
| Fitting, socle | C22×C33×C5 ⋊ C3 |
| derived, Sylow | C22 ⋊ C34×C5 |
| Hall | C22×C5 ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33×C5 | A4 |
| commutator, cosocle, hypocenter | C22 | C34×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C5 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C33×C5 | |
904 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 467);