Finite Group DatabasebetaFinite Group Databasebeta| order | 31524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C71⋊#3866 |
| unambiguous semidirect product | C71⋊(C3×#3866) |
| Fitting, socle, Hall | C3×C37×C71 ⋊ C4 |
| derived, Hall | C37×C71 ⋊ C3×C4 |
| Hall | C3×C71 ⋊ #3866 |
| Hall | C3×C37 ⋊ Dic71 |
| Sylow | C71 ⋊ C3×#3866 |
| Sylow | C37 ⋊ C3×Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C71⋊#3866 |
| commutator, hypocenter | C37×C71 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C71 | C4 |
| prime radical | C3×C71×D37 | C2 |
| cosocle | C71×D37 | C2×C3 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7881 |
2139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31524, 21);