Finite Group DatabasebetaFinite Group Databasebeta| order | 31524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊(#3866⋊C3) |
| unambiguous semidirect product | (C71⋊#3866)⋊C3 |
| Fitting, socle, derived, Hall | C37×C71 ⋊ C3×C4 |
| Hall | C71⋊#3866 ⋊ C3 |
| Hall | C71×C37⋊C3 ⋊ C4 |
| Hall | C37⋊C3 ⋊ Dic71 |
| Sylow | C71 ⋊ #3866⋊C3 |
| Sylow | C37 ⋊ C3×Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C71 | C3×C4 |
| prime radical | C71×D37⋊C3 | C2 |
| cosocle | C71×D37 | C2×C3 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2627 |
Polycyclic presentation:
2,3,2,37,71|a^2=c,d^a=d^31,e^a=e^70,d^b=d^26,d^c=d^36435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31524, 15);