Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D5×C67⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C5×C67⋊C3) |
| unambiguous semidirect product | (D5×C67)⋊(C3×C5) |
| unambiguous semidirect product | (C5×D5×C67)⋊C3 |
| Fitting, socle, Hall | C52×C67 ⋊ C2×C3 |
| derived | C5×C67 ⋊ C2×C3×C5 |
| Hall | C52×C67⋊C3 ⋊ C2 |
| Hall | C5×D5×C67 ⋊ C3 |
| Sylow | C67 ⋊ C3×C5×D5 |
| Sylow | C52 ⋊ C2×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×C67⋊C3 |
| commutator, cosocle, hypocenter | C5×C67 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C67 | C2×C3 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
500 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 16);