Finite Group DatabasebetaFinite Group Databasebeta| order | 30020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1501 |
| unambiguous semidirect product | C19⋊(C5×Dic79) |
| unambiguous semidirect product | C79⋊(C5×Dic19) |
| derived, Hall | C19×C79 ⋊ C4×C5 |
| Hall | C5×C19×C79 ⋊ C4 |
| Hall | C5×C79 ⋊ Dic19 |
| Hall | C5×C19 ⋊ Dic79 |
| Sylow | C79 ⋊ C5×Dic19 |
| Sylow | C19 ⋊ C5×Dic79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1501 |
| commutator, hypocenter | C19×C79 | C4×C5 |
| Frattini | C2 | C5×D1501 |
| Fitting, socle, prime radical | C2×C5×C19×C79 | C2 |
| cosocle | C2×C19×C79 | C2×C5 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30020 |
7520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30020, 4);