Finite Group DatabasebetaFinite Group Databasebeta| order | 760 |
| isoclinism | isoclinic class of D5×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic5×D19 |
| derived, Hall | C5×C19 ⋊ C2×C4 |
| Sylow | C19 ⋊ C2×Dic5 |
| Sylow | C5 ⋊ C4×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D19 |
| commutator, hypocenter | C5×C19 | C2×C4 |
| Fitting, socle, cosocle | C2×C5×C19 | C22 |
| prime radical | C2×C5×D19 | C2 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 380 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#170, #13095109, D19×Dic10, … |
| maximal normal subgroup of | D19×#170, #13095109, D19×Dic10, … |
| maximal quotient of | D19×#168, #13095026, Dic5×Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(760, 7);