Finite Group DatabasebetaFinite Group Databasebeta| order | 732 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C61 · Schur multiplier (H2) = C2 |
| direct product | A4×C61 |
| unambiguous semidirect product | C22⋊(C3×C61) |
| Fitting, socle, Hall | C22×C61 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C22×C61 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C61 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 244 |
244 conjugacy classes — view the full character table.
| derived subgroup of | A4⋊D61 |
| maximal subgroup of | S4×C61, A4⋊D61, A4×D61, … |
| maximal normal subgroup of | S4×C61, A4⋊D61, A4×D61, … |
| maximal quotient of | SL(2,𝔽3)×C61, C2×A4×C61, C22⋊C9×C61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(732, 13);