Finite Group DatabasebetaFinite Group Databasebeta| order | 31734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C41 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C41×C43 ⋊ C2×C3 |
| derived, Sylow | C43 ⋊ C2×C32×C41 |
| Hall | C3×C41×C43⋊C3 ⋊ C2 |
| Hall | C41×D43 ⋊ C32 |
| Hall | C41×C43 ⋊ C2×C32 |
| Hall | C3×C43⋊C3 ⋊ C2×C41 |
| Hall | D43 ⋊ C32×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | D43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C2×C32×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C43 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C41 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5289 |
1599 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31734, 14);