Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | D11×C29⋊C49 |
| unambiguous semidirect product | C11⋊(C2×C29⋊C49) |
| unambiguous semidirect product | (D11×C29)⋊C49 |
| derived, Hall | C11×C29 ⋊ C2×C49 |
| Hall | C11×C29⋊C49 ⋊ C2 |
| Hall | D11×C29 ⋊ C49 |
| Sylow | C29 ⋊ D11×C49 |
| Sylow | C11 ⋊ C2×C29⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | D11×C29⋊C7 |
| commutator, hypocenter | C11×C29 | C2×C49 |
| Fitting, socle, cosocle | C7×C11×C29 | C2×C7 |
| prime radical | C7×D11×C29 | C7 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15631 |
539 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 11);