Finite Group DatabasebetaFinite Group Databasebeta| order | 1170 |
| isoclinism | isoclinic class of C5⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D13⋊C9) |
| unambiguous semidirect product | (C13⋊C9)⋊D5 |
| unambiguous semidirect product | D65⋊C9 |
| derived, Hall | C5×C13 ⋊ C2×C9 |
| Hall | C5×C13⋊C9 ⋊ C2 |
| Hall | D65 ⋊ C9 |
| Hall | C13⋊C9 ⋊ D5 |
| Sylow | C13 ⋊ C9×D5 |
| Sylow | C5 ⋊ D13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(D13⋊C3) |
| commutator, hypocenter | C5×C13 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C13 | C2×C3 |
| prime radical | C3×D65 | C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 585 |
Polycyclic presentation:
2,3^2,5,13|b^3=c,d^a=d^4,e^a=e^12,e^b=e^366 conjugacy classes — view the full character table.
| maximal subgroup of | #63122⋊C9, #63121⋊C9, D5×D13⋊C9, … |
| maximal normal subgroup of | #63122⋊C9, #63121⋊C9, D5×D13⋊C9, … |
| maximal quotient of | Dic65⋊C9, C2×C5⋊(D13⋊C9), C11×C5⋊(D13⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1170, 3);