Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of C5⋊(C5⋊(D13⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊(D13⋊C3)) |
| unambiguous semidirect product | (C13⋊C3)⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C2×C3 |
| Hall | C52×C13⋊C3 ⋊ C2 |
| Hall | C5⋊D65 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ C3×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
Polycyclic presentation:
2,3,5^2,13|c^a=c^4,d^a=d^4,e^a=e^12,e^b=e^992 conjugacy classes — view the full character table.
| maximal subgroup of | #16839081, #16839082, #13049931⋊C3, … |
| maximal normal subgroup of | #16839081, #16839082, #13049931⋊C3, … |
| maximal quotient of | #16839052, C2×C5⋊(C5⋊(D13⋊C3)), C7×C5⋊(C5⋊(D13⋊C3)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 19);