Finite Group DatabasebetaFinite Group Databasebeta| order | 5820 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C97 · Schur multiplier (H2) = C2 |
| direct product | C5×A4×C97 |
| unambiguous semidirect product | C22⋊(C3×C5×C97) |
| unambiguous semidirect product | (C22×C5)⋊(C3×C97) |
| Fitting, socle, Hall | C22×C5×C97 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C5×C97 |
| Hall | C22×C97 ⋊ C3×C5 |
| Hall | C22×C5 ⋊ C3×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C97 | A4 |
| commutator, hypocenter | C22 | C3×C5×C97 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C97 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C5×C97 | |
20 conjugacy classes of subgroups.
1940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×A4×C97⋊C3, C3×C5×A4×C97, A4×C25×C97, … |
| maximal normal subgroup of | C5×A4×C97⋊C3, C3×C5×A4×C97, A4×C25×C97, … |
| maximal quotient of | C5×C22⋊C9×C97, C3×C5×A4×C97, A4×C25×C97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5820, 44);