Finite Group DatabasebetaFinite Group Databasebeta| order | 780 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×Dic5 |
| derived, Sylow | C5 ⋊ C3×C4×C13 |
| Hall | C3×C5×C13 ⋊ C4 |
| Hall | C5×C13 ⋊ C3×C4 |
| Hall | C3×C5 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | D5 |
| commutator, hypocenter | C5 | C3×C4×C13 |
| Frattini | C2 | C3×D5×C13 |
| Fitting, socle, prime radical | C2×C3×C5×C13 | C2 |
| cosocle | C2×C5 | C2×C3×C13 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C3×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 780 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×#170, C3×#10587064, C13×C3⋊#170, … |
| maximal normal subgroup of | C3×C13×#170, C3×#10587064, C13×C3⋊#170, … |
| maximal quotient of | C3×C13×#168, C2×C3×C13×Dic5, C9×C13×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(780, 6);