Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊D335) |
| unambiguous semidirect product | C5⋊D1005 |
| unambiguous semidirect product | C67⋊(C3⋊(C5⋊D5)) |
| Fitting, socle, derived, Hall | C3×C52×C67 ⋊ C2 |
| Hall | C52×C67 ⋊ D3 |
| Hall | C3×C67 ⋊ C5⋊D5 |
| Hall | C3×C52 ⋊ D67 |
| Sylow | C67 ⋊ C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ D201 |
| Sylow | C3 ⋊ C5⋊D335 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C67 | C2 |
| LCS | G ▷ C3×C52×C67 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,67|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^662514 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1005, D15×D335, D67×C3⋊(C5⋊D5), … |
| maximal normal subgroup of | D5×D1005, D15×D335, D67×C3⋊(C5⋊D5), … |
| maximal quotient of | C3⋊(C67⋊#1039), C2×C3⋊(C5⋊D335), C5⋊D3015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 30);