Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C11⋊#63122 |
| unambiguous semidirect product | C11⋊(C11×#63122) |
| Fitting, socle, Hall | C5×C112×C13 ⋊ C4 |
| derived | C5×C11×C13 ⋊ C4×C11 |
| Hall | C112×C13 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ #261 |
| Sylow | C112 ⋊ #63122 |
| Hall | C5×C13 ⋊ C11×Dic11 |
| Sylow | C13 ⋊ C11×C11⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C11×C11⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C11⋊#63122 |
| commutator, hypocenter | C5×C11×C13 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C13 | C4 |
| prime radical | C112×D65 | C2 |
| cosocle | C11×D65 | C2×C11 |
| LCS | G ▷ C5×C11×C13 | |
| UCS | C1 ◁ C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1430 |
2090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 189);