Finite Group DatabasebetaFinite Group Databasebeta| order | 30690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (ΓL(1,𝔽32)⋊C9)⋊D11 |
| unambiguous semidirect product | (ΓL(1,𝔽32)⋊D11)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ((C31⋊C3)⋊C5)⋊D11 |
| commutator, hypocenter | C11×C31 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C11×C31 | C2×C3×C5 |
| prime radical | C3×ΓL(1,𝔽32)⋊D11 | C3 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
Polycyclic presentation:
2,3,5,11,31,3|b^3=f,d^a=d^10,e^a=e^30,e^b=e^25,e^c=e^16348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30690, 91);