Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of C3⋊(C5⋊D65) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊D65) |
| unambiguous semidirect product | C5⋊D195 |
| unambiguous semidirect product | C13⋊(C3⋊(C5⋊D5)) |
| Fitting, socle, derived, Hall | C3×C52×C13 ⋊ C2 |
| Hall | C52×C13 ⋊ D3 |
| Hall | C3×C52 ⋊ D13 |
| Hall | C3×C13 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D39 |
| Sylow | C13 ⋊ C3⋊(C5⋊D5) |
| Sylow | C3 ⋊ C5⋊D65 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C13 | C2 |
| LCS | G ▷ C3×C52×C13 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 975 |
Polycyclic presentation:
2,3,5^2,13|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^12489 conjugacy classes — view the full character table.
| maximal subgroup of | D13×C3⋊(C5⋊D5), C5⋊D5×D39, D3×C5⋊D65, … |
| maximal normal subgroup of | D13×C3⋊(C5⋊D5), C5⋊D5×D39, D3×C5⋊D65, … |
| maximal quotient of | C3⋊#13049918, C2×C3⋊(C5⋊D65), C3⋊(C5⋊D455), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 39);