Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | D23×C52⋊C9 |
| unambiguous semidirect product | C23⋊(C2×C52⋊C9) |
| unambiguous semidirect product | (C52×D23)⋊C9 |
| derived, Hall | C52×C23 ⋊ C2×C9 |
| Hall | C23×C52⋊C9 ⋊ C2 |
| Hall | C52×D23 ⋊ C9 |
| Sylow | C52 ⋊ C9×D23 |
| Sylow | C23 ⋊ C2×C52⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D23×C52⋊C3 |
| commutator, hypocenter | C52×C23 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C23 | C2×C3 |
| prime radical | C3×C52×D23 | C3 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#90646, D23×(C5⋊D5)⋊C9, C2×D23×C52⋊C9 |
| maximal normal subgroup of | D23×#90646, D23×(C5⋊D5)⋊C9, C2×D23×C52⋊C9 |
| maximal quotient of | Dic23×C52⋊C9, C2×D23×C52⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 26);