Finite Group DatabasebetaFinite Group Databasebeta| order | 10650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C71⋊C25 |
| unambiguous semidirect product | (C2×C71)⋊(C3×C25) |
| unambiguous semidirect product | (C2×C3×C71)⋊C25 |
| derived, Sylow | C71 ⋊ C2×C3×C25 |
| Hall | C2×C3×C71 ⋊ C25 |
| Hall | C3×C71 ⋊ C2×C25 |
| Hall | C2×C71 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C71⋊C5 |
| commutator, hypocenter | C71 | C2×C3×C25 |
| Frattini | C5 | C2×C3×C71⋊C5 |
| Fitting, socle, prime radical | C2×C3×C5×C71 | C5 |
| cosocle | C5×C71 | C2×C3×C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C3×C5 | |
24 conjugacy classes of subgroups.
570 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C71⋊C25, C3×Dic71⋊C25, Dic3×C71⋊C25, … |
| maximal normal subgroup of | C3×C4×C71⋊C25, C3×Dic71⋊C25, Dic3×C71⋊C25, … |
| maximal quotient of | C3×C4×C71⋊C25, C22×C3×C71⋊C25, C2×C9×C71⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10650, 2);