Finite Group DatabasebetaFinite Group Databasebeta| order | 7692 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C641 · Schur multiplier (H2) = C2 |
| direct product | A4×C641 |
| unambiguous semidirect product | C22⋊(C3×C641) |
| unambiguous semidirect product | (C22×C641)⋊C3 |
| Fitting, socle, Hall | C22×C641 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C641 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C641 | A4 |
| commutator, hypocenter | C22 | C3×C641 |
| Frattini | C1 | G |
| Fitting, socle | C22×C641 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C641 | |
10 conjugacy classes of subgroups.
2564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×A4×C641, A4×C641⋊C5, C5×A4×C641, … |
| maximal normal subgroup of | C3×A4×C641, A4×C641⋊C5, C5×A4×C641 |
| maximal quotient of | C22⋊C9×C641, C3×A4×C641, C5×A4×C641 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7692, 9);