Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13×C19 ⋊ C2×C9 |
| Hall | #29509854 ⋊ C2 |
| Hall | D1729 ⋊ C9 |
| Hall | C13×C19 ⋊ D7⋊C9 |
| Hall | C7×C19 ⋊ D13⋊C9 |
| Hall | C7×C13 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ #13109902 |
| Sylow | C13 ⋊ #14558801 |
| Sylow | C7 ⋊ #17984638 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C19 | C2×C9 |
| prime radical | (C19⋊C3)⋊D91 | 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,d^a=d^6,e^a=e^12,f^a=f^18,d^b=d^2,e^b=e^3,f^b=f^4,f^c=f^7154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 140);