Finite Group DatabasebetaFinite Group Databasebeta| order | 30246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5041 · Schur multiplier (H2) = C1 |
| direct product | D3×C5041 |
| unambiguous semidirect product | C3⋊(C2×C5041) |
| Fitting, Hall | C3×C5041 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5041 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5041 | D3 |
| commutator, hypocenter | C3 | C2×C5041 |
| Frattini | C71 | D3×C71 |
| Fitting | C3×C5041 | C2 |
| socle, cosocle | C3×C71 | C2×C71 |
| prime radical | D3×C71 | C71 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C5041 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15123 |
15123 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30246, 2);