Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×#63121 |
| Fitting, Hall | C5×C13×C121 ⋊ C4 |
| derived, Hall | C5×C13 ⋊ C4×C121 |
| Hall | C13×C121 ⋊ AGL(1,𝔽5) |
| Hall | C5×C121 ⋊ #261 |
| Sylow | C13 ⋊ AGL(1,𝔽5)×C121 |
| Sylow | C5 ⋊ #261×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | #63121 |
| commutator, hypocenter | C5×C13 | C4×C121 |
| Frattini | C11 | C11×#63121 |
| Fitting | C5×C13×C121 | C4 |
| socle | C5×C11×C13 | C4×C11 |
| prime radical, cosocle | C11×D65 | C2×C11 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C121 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
2420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 26);