Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×D23×C52⋊C3 |
| unambiguous semidirect product | C23⋊(C2×C3×C52⋊C3) |
| unambiguous semidirect product | (C52×D23)⋊C32 |
| unambiguous semidirect product | (C3×C52×D23)⋊C3 |
| Fitting, socle | C3×C52×C23 ⋊ C2×C3 |
| derived, Hall | C52×C23 ⋊ C2×C32 |
| Hall | C3×C23×C52⋊C3 ⋊ C2 |
| Hall | C52×D23 ⋊ C32 |
| Sylow | C52 ⋊ C32×D23 |
| Sylow | C23 ⋊ C2×C3×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D23×C52⋊C3 |
| commutator, cosocle, hypocenter | C52×C23 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C23 | C2×C3 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D23×#3874, C3×D23×(C5⋊D5)⋊C3, D23×C3⋊#3874, … |
| maximal normal subgroup of | C3×D23×#3874, C3×D23×(C5⋊D5)⋊C3, D23×C3⋊#3874, … |
| maximal quotient of | C3×C52⋊C3×Dic23, C2×C3×D23×C52⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 44);