Finite Group DatabasebetaFinite Group Databasebeta| order | 760 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#170 |
| derived, Sylow | C5 ⋊ C8×C19 |
| Hall | C5×C19 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C8×C19 |
| Frattini | C2 | C19×AGL(1,𝔽5) |
| Fitting, socle, prime radical | C2×C5×C19 | C4 |
| cosocle | Dic5 | C2×C19 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 760 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#170, #13095108, #13095109, … |
| maximal normal subgroup of | D19×#170, #13095108, #13095109, … |
| maximal quotient of | C19×#674, C2×C19×#170 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(760, 5);