Finite Group DatabasebetaFinite Group Databasebeta| order | 34572 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C2 |
| direct product | C43×C22⋊(C67⋊C3) |
| unambiguous semidirect product | C22⋊(C43×C67⋊C3) |
| unambiguous semidirect product | C67⋊(A4×C43) |
| Fitting, socle, Hall | C22×C43×C67 ⋊ C3 |
| derived, Hall | C22×C67 ⋊ C3×C43 |
| Hall | C43×C67 ⋊ A4 |
| Hall | C22×C43 ⋊ C67⋊C3 |
| Sylow | C67 ⋊ A4×C43 |
| Sylow | C22 ⋊ C43×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C22⋊(C67⋊C3) |
| commutator, cosocle, hypocenter | C22×C67 | C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C22×C43×C67 | C3 |
| LCS | G ▷ C22×C67 | |
| UCS | C1 ◁ C43 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11524 |
3956 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34572, 50);