Finite Group DatabasebetaFinite Group Databasebeta| order | 31524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊(Dic37⋊C3) |
| unambiguous semidirect product | Dic2627⋊C3 |
| derived, Hall | C37×C71 ⋊ C3×C4 |
| Hall | Dic2627 ⋊ C3 |
| Hall | C71×C37⋊C3 ⋊ C4 |
| Hall | C37⋊C3 ⋊ Dic71 |
| Sylow | C71 ⋊ Dic37⋊C3 |
| Sylow | C37 ⋊ C3×Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C71⋊(D37⋊C3) |
| commutator, hypocenter | C37×C71 | C3×C4 |
| Fitting, socle, cosocle | C2×C37×C71 | C2×C3 |
| prime radical | C2×C71×C37⋊C3 | C2 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10508 |
Polycyclic presentation:
2,3,37,71,2|a^2=e,c^a=c^36,d^a=d^70,c^b=c^261074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31524, 12);