Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5187 |
| unambiguous semidirect product | C7⋊(C3⋊D741) |
| unambiguous semidirect product | C13⋊(C3⋊D399) |
| unambiguous semidirect product | C19⋊(C3⋊D273) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C13×C19 | C2 |
| LCS | G ▷ C32×C7×C13×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15561 |
Polycyclic presentation:
2,3^2,7,13,19|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^12,f^a=f^187782 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 528);