Finite Group DatabasebetaFinite Group Databasebeta| order | 31260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#14523438⋊C5) |
| unambiguous semidirect product | (C3⋊#14523438)⋊C5 |
| Fitting, socle, derived, Hall | C3×C521 ⋊ C4×C5 |
| Hall | C3×C521⋊C5 ⋊ C4 |
| Hall | C3⋊#14523438 ⋊ C5 |
| Hall | C521⋊C5 ⋊ Dic3 |
| Sylow | C521 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ #14523438⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C521 | C4×C5 |
| prime radical | C3×D521⋊C5 | C2 |
| cosocle | C3×D521 | C2×C5 |
| LCS | G ▷ C3×C521 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1563 |
Polycyclic presentation:
2,5,2,3,521|a^2=c,d^a=d^2,e^a=e^235,e^b=e^104,e^c=e^520108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31260, 15);