Finite Group DatabasebetaFinite Group Databasebeta| order | 7596 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C211 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×C211 |
| unambiguous semidirect product | C22⋊(C32×C211) |
| unambiguous semidirect product | (C22×C3)⋊(C3×C211) |
| Fitting, socle | C22×C3×C211 ⋊ C3 |
| derived, Sylow | C22 ⋊ C32×C211 |
| Hall | C22×C211 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C211 | A4 |
| commutator, hypocenter | C22 | C32×C211 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C211 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C211 | |
28 conjugacy classes of subgroups.
2532 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×A4×C211⋊C5, C3×C5×A4×C211, C3×A5×C211 |
| maximal normal subgroup of | C3×A4×C211⋊C5, C3×C5×A4×C211 |
| maximal quotient of | C3×C5×A4×C211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7596, 40);