Finite Group DatabasebetaFinite Group Databasebeta| order | 14820 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C5×C19×#261) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C4×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C19 | C4 |
| prime radical | C3×C5×C19×D13 | C2 |
| cosocle | C3×D13 | C2×C5×C19 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C5×C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3705 |
1425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14820, 174);