Finite Group DatabasebetaFinite Group Databasebeta| order | 760 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C19×Dic5 |
| derived, Sylow | C5 ⋊ C2×C4×C19 |
| Hall | C5×C19 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C19 | D5 |
| commutator, hypocenter | C5 | C2×C4×C19 |
| Frattini | C2 | C2×D5×C19 |
| Fitting, socle, prime radical | C22×C5×C19 | C2 |
| cosocle | C2×C5 | C22×C19 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 760 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic5×Dic19, (C2×D19)⋊Dic5, #13095044, … |
| maximal normal subgroup of | Dic5×Dic19, (C2×D19)⋊Dic5, #13095044, … |
| maximal quotient of | C2×C19×#168, C19×#681, C4×C19×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(760, 22);