Finite Group DatabasebetaFinite Group Databasebeta| order | 30020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D19×D79 |
| unambiguous semidirect product | (D19×C79)⋊(C2×C5) |
| unambiguous semidirect product | (C19×D79)⋊(C2×C5) |
| unambiguous semidirect product | D1501⋊(C2×C5) |
| Fitting, socle, Hall | C5×C19×C79 ⋊ C22 |
| derived, Hall | C19×C79 ⋊ C22×C5 |
| Hall | C5×C79 ⋊ C2×D19 |
| Hall | C5×C19 ⋊ C2×D79 |
| Sylow | C79 ⋊ C2×C5×D19 |
| Sylow | C19 ⋊ C2×C5×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D19×D79 |
| commutator, cosocle, hypocenter | C19×C79 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C79 | C22 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7505 |
2255 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30020, 10);