Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D29⋊C49) |
| unambiguous semidirect product | D319⋊C49 |
| unambiguous semidirect product | (C29⋊C49)⋊D11 |
| derived, Hall | C11×C29 ⋊ C2×C49 |
| Hall | C11×C29⋊C49 ⋊ C2 |
| Hall | C29⋊C49 ⋊ D11 |
| Hall | D319 ⋊ C49 |
| Sylow | C29 ⋊ D11×C49 |
| Sylow | C11 ⋊ D29⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | C11⋊(D29⋊C7) |
| commutator, hypocenter | C11×C29 | C2×C49 |
| Fitting, socle, cosocle | C7×C11×C29 | C2×C7 |
| prime radical | C7×D319 | C7 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15631 |
Polycyclic presentation:
2,7,11,29,7|b^7=e,c^a=c^10,d^a=d^28,d^b=d^16497 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 12);