Finite Group DatabasebetaFinite Group Databasebeta| order | 1755 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×C13⋊C9 |
| unambiguous semidirect product | (C3×C13)⋊(C5×C9) |
| unambiguous semidirect product | (C3×C5×C13)⋊C9 |
| derived, Sylow | C13 ⋊ C3×C5×C9 |
| Hall | C5×C13 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C5×C9 |
| Frattini | C3 | C3×C5×C13⋊C3 |
| Fitting, socle, prime radical | C32×C5×C13 | C3 |
| cosocle | C3×C13 | C32×C5 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C32×C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1755 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1755, 6);