Finite Group DatabasebetaFinite Group Databasebeta| order | 18620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D19×D49 |
| unambiguous semidirect product | (C19×D49)⋊(C2×C5) |
| unambiguous semidirect product | (D19×C49)⋊(C2×C5) |
| unambiguous semidirect product | D931⋊(C2×C5) |
| Fitting, Hall | C5×C19×C49 ⋊ C22 |
| derived, Hall | C19×C49 ⋊ C22×C5 |
| Hall | C5×C49 ⋊ C2×D19 |
| Hall | C5×C19 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×C5×D19 |
| Sylow | C19 ⋊ C2×C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D19×D49 |
| commutator, cosocle, hypocenter | C19×C49 | C22×C5 |
| Frattini | C7 | C5×D7×D19 |
| Fitting | C5×C19×C49 | C22 |
| socle | C5×C7×C19 | C2×D7 |
| LCS | G ▷ C19×C49 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4655 |
1430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18620, 10);