Finite Group DatabasebetaFinite Group Databasebeta| order | 6420 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C107 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C5×C107 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C5×C107 |
| Hall | C22×C107 ⋊ C3×C5 |
| Hall | C22×C5 ⋊ C3×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C107 | A4 |
| commutator, hypocenter | C22 | C3×C5×C107 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C107 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C5×C107 | |
20 conjugacy classes of subgroups.
2140 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×A4×C107, A4×C25×C107, C52×A4×C107, … |
| maximal normal subgroup of | C3×C5×A4×C107, A4×C25×C107, C52×A4×C107 |
| maximal quotient of | C5×C22⋊C9×C107, C3×C5×A4×C107, A4×C25×C107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6420, 21);