Finite Group DatabasebetaFinite Group Databasebeta| order | 30690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#16811771 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C11×C31 | C2×C5 |
| Frattini | C3 | C3⋊#16811771 |
| socle | C3×C11×C31 | C5×D3 |
| LCS | G ▷ C9×C11×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
Polycyclic presentation:
2,3,5,11,31,3|b^3=f^2,b^a=b^2f,e^a=e^30,f^a=f^2,d^c=d^4,e^c=e^16339 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30690, 56);