Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C73 · Schur multiplier (H2) = C2 |
| direct product | C73×C22⋊(C37⋊C3) |
| unambiguous semidirect product | C22⋊(C73×C37⋊C3) |
| unambiguous semidirect product | C37⋊(A4×C73) |
| Fitting, socle, Hall | C22×C37×C73 ⋊ C3 |
| derived, Hall | C22×C37 ⋊ C3×C73 |
| Hall | C37×C73 ⋊ A4 |
| Hall | C22×C73 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ A4×C73 |
| Sylow | C22 ⋊ C73×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | C22⋊(C37⋊C3) |
| commutator, cosocle, hypocenter | C22×C37 | C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C22×C37×C73 | C3 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C73 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10804 |
3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 87);