Finite Group DatabasebetaFinite Group Databasebeta| order | 30690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(ΓL(1,𝔽32)⋊D11) |
| unambiguous semidirect product | C3⋊(C3×ΓL(1,𝔽32)⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(ΓL(1,𝔽32)⋊D11) |
| commutator, cosocle, hypocenter | C3×C11×C31 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C31 | C2×C5 |
| LCS | G ▷ C3×C11×C31 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2046 |
567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30690, 186);