Finite Group DatabasebetaFinite Group Databasebeta| order | 4350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D725 |
| unambiguous semidirect product | C25⋊(C3×D29) |
| unambiguous semidirect product | C29⋊(C3×D25) |
| Fitting, Hall | C3×C25×C29 ⋊ C2 |
| derived, Hall | C25×C29 ⋊ C2×C3 |
| Hall | C3×C29 ⋊ D25 |
| Hall | C3×C25 ⋊ D29 |
| Sylow | C29 ⋊ C3×D25 |
| Sylow | C25 ⋊ C3×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D725 |
| commutator, cosocle, hypocenter | C25×C29 | C2×C3 |
| Frattini | C5 | C3×D145 |
| Fitting | C3×C25×C29 | C2 |
| socle | C3×C5×C29 | D5 |
| LCS | G ▷ C25×C29 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2175 |
1092 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D725, C32×D725, C3×D2175, … |
| maximal normal subgroup of | C9×D725, C32×D725, C3×C7×D725, … |
| maximal quotient of | C9×D725, C32×D725, C3×D2175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4350, 4);