Finite Group DatabasebetaFinite Group Databasebeta| order | 760 |
| isoclinism | isoclinic class of D95 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#168 |
| derived, Hall | C5×C19 ⋊ C8 |
| Sylow | C19 ⋊ #168 |
| Sylow | C5 ⋊ C19⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D95 |
| commutator, hypocenter | C5×C19 | C8 |
| Fitting, cosocle | C4×C5×C19 | C2 |
| socle, prime radical | C2×C5×C19 | C4 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 760 |
Polycyclic presentation:
2^3,5,19|a^2=b,b^2=c,d^a=d^4,e^a=e^18196 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#168, D5×C19⋊C8, #13095026, … |
| maximal normal subgroup of | D19×#168, D5×C19⋊C8, #13095026, … |
| maximal quotient of | C19⋊#672, C2×C19⋊#168 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(760, 3);