Finite Group DatabasebetaFinite Group Databasebeta| order | 1170 |
| isoclinism | isoclinic class of C5⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C5⋊(D13⋊C3) |
| unambiguous semidirect product | C5⋊(C3×D13⋊C3) |
| unambiguous semidirect product | (C13⋊C3)⋊(C3×D5) |
| unambiguous semidirect product | D65⋊C32 |
| unambiguous semidirect product | (C3×D65)⋊C3 |
| Fitting, socle | C3×C5×C13 ⋊ C2×C3 |
| derived, Hall | C5×C13 ⋊ C2×C32 |
| Hall | C3×C5×C13⋊C3 ⋊ C2 |
| Hall | D65 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ D5 |
| Sylow | C13 ⋊ C32×D5 |
| Sylow | C5 ⋊ C3×D13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊(D13⋊C3) |
| commutator, cosocle, hypocenter | C5×C13 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 195 |
66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1170, 15);