Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×D69 |
| unambiguous semidirect product | C3⋊(D23×C52⋊C3) |
| unambiguous semidirect product | C23⋊(D3×C52⋊C3) |
| unambiguous semidirect product | (C52×D69)⋊C3 |
| Fitting, socle, derived | C3×C52×C23 ⋊ C2×C3 |
| Hall | C3×C23×C52⋊C3 ⋊ C2 |
| Hall | C52×C23 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ D23 |
| Sylow | C52 ⋊ C3×D69 |
| Sylow | C23 ⋊ D3×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C23 | C2×C3 |
| LCS | G ▷ C3×C52×C23 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
396 conjugacy classes — view the full character table.
| maximal subgroup of | D69×#3874, D69⋊#3874, D3×D23×C52⋊C3, … |
| maximal normal subgroup of | D69×#3874, D69⋊#3874, D3×D23×C52⋊C3, … |
| maximal quotient of | C52⋊C3×Dic69, C2×C52⋊C3×D69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 50);