Finite Group DatabasebetaFinite Group Databasebeta| order | 30690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1705 |
| unambiguous semidirect product | C5⋊(C9×D341) |
| unambiguous semidirect product | C11⋊(C9×D155) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1705 |
| commutator, hypocenter | C5×C11×C31 | C2×C9 |
| Frattini | C3 | C3×D1705 |
| Fitting | C5×C9×C11×C31 | C2 |
| socle, cosocle | C3×C5×C11×C31 | C2×C3 |
| prime radical | C3×D1705 | C3 |
| LCS | G ▷ C5×C11×C31 | |
| UCS | C1 ◁ C9 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15345 |
7686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30690, 21);