Finite Group DatabasebetaFinite Group Databasebeta| order | 31570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#17985238 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C41 | C2×C5 |
| LCS | G ▷ C7×C11×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3157 |
Polycyclic presentation:
2,5,7,11,41|c^a=c^6,e^a=e^40,d^b=d^4,e^b=e^37343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31570, 52);