Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | (C13⋊C3)⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C5⋊(C5⋊(D13⋊C3)))⋊C3 |
| unambiguous semidirect product | #14519613⋊C3 |
| unambiguous semidirect product | #14519615⋊C3 |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C2×C32 |
| Hall | C13⋊C3×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D65 ⋊ C32 |
| Sylow | C52 ⋊ C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×(C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C13 | C2×C32 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5^2,13|d^a=d^4,e^a=e^4,f^a=f^12,f^b=f^3,d^c=de,e^c=d^2e^352 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊(D13⋊C3), #16839082⋊C3, #16839081⋊C3, … |
| maximal normal subgroup of | #3874⋊(D13⋊C3), #16839082⋊C3, #16839081⋊C3, … |
| maximal quotient of | #16839052⋊C3, C2×(C13⋊C3)⋊((C5⋊D5)⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 64);