Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C19 | C2×C9 |
| prime radical | C7×D13×C19⋊C3 | C3 |
| cosocle | C7×C13×C19⋊C3 | C2×C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1729 |
Polycyclic presentation:
2,3^2,7,13,19|b^3=c,e^a=e^12,d^b=d^2,e^b=e^3,f^b=f^4,f^c=f^7184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 211);