Finite Group DatabasebetaFinite Group Databasebeta| order | 30690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | D11×ΓL(1,𝔽32)⋊C9 |
| unambiguous semidirect product | (D11×ΓL(1,𝔽32))⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D11×(C31⋊C3)⋊C5 |
| commutator, hypocenter | C11×C31 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C11×C31 | C2×C3×C5 |
| prime radical | C3×D11×ΓL(1,𝔽32) | C3 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
357 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30690, 85);