Finite Group DatabasebetaFinite Group Databasebeta| order | 31524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C3⋊#3866 |
| unambiguous semidirect product | C3⋊(C71×#3866) |
| Fitting, socle, Hall | C3×C37×C71 ⋊ C4 |
| derived, Hall | C3×C37 ⋊ C4×C71 |
| Hall | C37×C71 ⋊ Dic3 |
| Hall | C3×C71 ⋊ #3866 |
| Sylow | C37 ⋊ Dic3×C71 |
| Sylow | C3 ⋊ C71×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C3⋊#3866 |
| commutator, hypocenter | C3×C37 | C4×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C71 | C4 |
| prime radical | C3×C71×D37 | C2 |
| cosocle | C3×D37 | C2×C71 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C71 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7881 |
2343 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31524, 24);