Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊(D67⋊C3)) |
| unambiguous semidirect product | (C67⋊C3)⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C67 ⋊ C2×C3 |
| Hall | C52×C67⋊C3 ⋊ C2 |
| Hall | C5⋊D335 ⋊ C3 |
| Hall | C67⋊C3 ⋊ C5⋊D5 |
| Sylow | C67 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C67 | C2×C3 |
| LCS | G ▷ C52×C67 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,67|c^a=c^4,d^a=d^4,e^a=e^66,e^b=e^29317 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 17);