Finite Group DatabasebetaFinite Group Databasebeta| order | 31668 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊(D29⋊C7) |
| unambiguous semidirect product | (C3⋊(D29⋊C7))⋊D13 |
| unambiguous semidirect product | (D39⋊D29)⋊C7 |
| unambiguous semidirect product | (C13⋊(D29⋊C7))⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C29 | C22×C7 |
| LCS | G ▷ C3×C13×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1131 |
Polycyclic presentation:
2^2,7,3,13,29|e^a=e^12,f^a=f^28,d^b=d^2,e^b=e^12,f^c=f^16210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31668, 89);