Finite Group DatabasebetaFinite Group Databasebeta| order | 31734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C3 |
| direct product | C43×C3⋊D123 |
| unambiguous semidirect product | C3⋊(C43×D123) |
| unambiguous semidirect product | C41⋊(C3⋊D3×C43) |
| Fitting, socle, Hall | C32×C41×C43 ⋊ C2 |
| derived, Hall | C32×C41 ⋊ C2×C43 |
| Hall | C41×C43 ⋊ C3⋊D3 |
| Hall | C32×C43 ⋊ D41 |
| Sylow | C41 ⋊ C3⋊D3×C43 |
| Sylow | C32 ⋊ C43×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C3⋊D123 |
| commutator, cosocle, hypocenter | C32×C41 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C32×C41×C43 | C2 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C43 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15867 |
7998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31734, 31);