Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D5×#10597244 |
| unambiguous semidirect product | C5⋊(C2×#10597244) |
| Fitting, socle, derived | C5×C112 ⋊ C2×C5 |
| Hall | C5×#10597244 ⋊ C2 |
| Sylow | C112 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C112 | C2×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
116 conjugacy classes — view the full character table.
| maximal subgroup of | #27130895, #27130898, #27130899, … |
| maximal normal subgroup of | #27130895, #27130898, #27130899, … |
| maximal quotient of | Dic5×#10597244, C2×D5×#10597244, C3×D5×#10597244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 66);