Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C49 · Schur multiplier (H2) = C1 |
| direct product | C11×D29⋊C49 |
| unambiguous semidirect product | D29⋊(C11×C49) |
| unambiguous semidirect product | (C11×D29)⋊C49 |
| unambiguous semidirect product | (C29⋊C49)⋊(C2×C11) |
| derived, Sylow | C29 ⋊ C2×C11×C49 |
| Hall | C11×C29⋊C49 ⋊ C2 |
| Hall | C29⋊C49 ⋊ C2×C11 |
| Hall | C11×D29 ⋊ C49 |
| Hall | C11×C29 ⋊ C2×C49 |
| Hall | D29 ⋊ C11×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | D29⋊C7 |
| commutator, hypocenter | C29 | C2×C11×C49 |
| Frattini | C7 | C11×D29⋊C7 |
| Fitting, socle | C7×C11×C29 | C2×C7 |
| prime radical | C7×C11×D29 | C7 |
| cosocle | C7×C29 | C2×C7×C11 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15631 |
1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 10);