Finite Group DatabasebetaFinite Group Databasebeta| order | 760 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C19×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C4×C19) |
| Fitting, socle | C2×C5×C19 ⋊ C4 |
| derived, Sylow | C5 ⋊ C2×C4×C19 |
| Hall | C5×C19 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C19 | C4 |
| prime radical | C2×D5×C19 | C2 |
| cosocle | D5 | C22×C19 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(760, 33);