Finite Group DatabasebetaFinite Group Databasebeta| order | 31620 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C3)⋊Dic85 |
| unambiguous semidirect product | Dic2635⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C17⋊(D31⋊C3)) |
| commutator, hypocenter | C5×C17×C31 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C17×C31 | C2×C3 |
| prime radical | C2×C5×C17×C31⋊C3 | C2 |
| LCS | G ▷ C5×C17×C31 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10540 |
Polycyclic presentation:
2,3,5,17,31,2|a^2=f,c^a=c^4,d^a=d^16,e^a=e^30,e^b=e^251114 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31620, 33);