Finite Group DatabasebetaFinite Group Databasebeta| order | 31122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊D247 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊D247 |
| 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^21866 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31122, 112);