Finite Group DatabasebetaFinite Group Databasebeta| order | 31260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic521⋊C5) |
| unambiguous semidirect product | Dic1563⋊C5 |
| derived, Hall | C3×C521 ⋊ C4×C5 |
| Hall | C3×C521⋊C5 ⋊ C4 |
| Hall | Dic1563 ⋊ C5 |
| Hall | C521⋊C5 ⋊ Dic3 |
| Sylow | C521 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ Dic521⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D521⋊C5) |
| commutator, hypocenter | C3×C521 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C521 | C2×C5 |
| prime radical | C2×C3×C521⋊C5 | C2 |
| LCS | G ▷ C3×C521 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6252 |
Polycyclic presentation:
2,3,5,521,2|a^2=e,b^a=b^2,d^a=d^520,d^c=d^25342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31260, 12);