Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C13×C19 ⋊ C2×C9 |
| Hall | #29509841 ⋊ C2 |
| Hall | D1729 ⋊ C9 |
| Hall | C13×C19 ⋊ D7⋊C9 |
| Hall | C7×C19 ⋊ D13⋊C9 |
| Hall | C7×C13 ⋊ #4294⋊C2 |
| Sylow | C19 ⋊ #13109902 |
| Sylow | C13 ⋊ #14558786 |
| Sylow | C7 ⋊ #17984623 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #23780625 |
| commutator, hypocenter | C7×C13×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C13×C19 | C2×C3 |
| prime radical | C3×D1729 | C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15561 |
Polycyclic presentation:
2,3,7,13,19,3|b^3=f,c^a=c^6,d^a=d^12,e^a=e^18,c^b=c^2,d^b=d^3,e^b=e^7882 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 116);