Finite Group DatabasebetaFinite Group Databasebeta| order | 31260 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic521⋊C5 |
| unambiguous semidirect product | Dic521⋊(C3×C5) |
| unambiguous semidirect product | (C3×Dic521)⋊C5 |
| derived, Sylow | C521 ⋊ C3×C4×C5 |
| Hall | C3×C521⋊C5 ⋊ C4 |
| Hall | C3×Dic521 ⋊ C5 |
| Hall | C521⋊C5 ⋊ C3×C4 |
| Hall | Dic521 ⋊ C3×C5 |
| Hall | C3×C521 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D521⋊C5 |
| commutator, hypocenter | C521 | C3×C4×C5 |
| Frattini | C2 | C3×D521⋊C5 |
| Fitting, socle | C2×C3×C521 | C2×C5 |
| prime radical | C2×C3×C521⋊C5 | C2 |
| cosocle | C2×C521 | C2×C3×C5 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6252 |
372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31260, 10);