Finite Group DatabasebetaFinite Group Databasebeta| order | 31218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C11⋊D473) |
| unambiguous semidirect product | C11⋊D1419 |
| unambiguous semidirect product | C43⋊(C3⋊(C11⋊D11)) |
| Fitting, socle, derived, Hall | C3×C112×C43 ⋊ C2 |
| Hall | C112×C43 ⋊ D3 |
| Hall | C3×C112 ⋊ D43 |
| Hall | C3×C43 ⋊ C11⋊D11 |
| Sylow | C112 ⋊ D129 |
| Sylow | C43 ⋊ C3⋊(C11⋊D11) |
| Sylow | C3 ⋊ C11⋊D473 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C112×C43 | C2 |
| LCS | G ▷ C3×C112×C43 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15609 |
Polycyclic presentation:
2,3,11^2,43|b^a=b^2,c^a=c^10,d^a=d^10,e^a=e^427806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31218, 40);