Finite Group DatabasebetaFinite Group Databasebeta| order | 19950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D175 |
| unambiguous semidirect product | C25⋊(D7×C19⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C19×C25 | C2×C3 |
| Frattini | C5 | C19⋊C3×D35 |
| socle | C5×C7×C19 | C3×D5 |
| LCS | G ▷ C7×C19×C25 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3325 |
801 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19950, 41);