Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of C25⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D13⋊C3) |
| unambiguous semidirect product | (C13⋊C3)⋊D25 |
| unambiguous semidirect product | D325⋊C3 |
| Fitting, derived, Hall | C13×C25 ⋊ C2×C3 |
| Hall | C25×C13⋊C3 ⋊ C2 |
| Hall | D325 ⋊ C3 |
| Hall | C13⋊C3 ⋊ D25 |
| Sylow | C25 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ C3×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C25 | C2×C3 |
| Frattini | C5 | C5⋊(D13⋊C3) |
| socle | C5×C13 | C3×D5 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 325 |
Polycyclic presentation:
2,3,5,13,5|c^5=e^4,c^a=c^4e,d^a=d^12,e^a=e^4,d^b=d^392 conjugacy classes — view the full character table.
| maximal subgroup of | #13049908⋊C3, #13049907⋊C3, D25×D13⋊C3, … |
| maximal normal subgroup of | #13049908⋊C3, #13049907⋊C3, D25×D13⋊C3, … |
| maximal quotient of | Dic325⋊C3, C2×C25⋊(D13⋊C3), C7×C25⋊(D13⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 3);