Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D67⋊C3) |
| unambiguous semidirect product | (C67⋊C3)⋊D25 |
| unambiguous semidirect product | D1675⋊C3 |
| Fitting, derived, Hall | C25×C67 ⋊ C2×C3 |
| Hall | C25×C67⋊C3 ⋊ C2 |
| Hall | D1675 ⋊ C3 |
| Hall | C67⋊C3 ⋊ D25 |
| Sylow | C67 ⋊ C3×D25 |
| Sylow | C25 ⋊ D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C67 | C2×C3 |
| Frattini | C5 | C5⋊(D67⋊C3) |
| socle | C5×C67 | C3×D5 |
| LCS | G ▷ C25×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,67,5|c^5=e^4,c^a=c^4e,d^a=d^66,e^a=e^4,d^b=d^37317 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 12);