Finite Group DatabasebetaFinite Group Databasebeta| order | 19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D127⋊C3 |
| unambiguous semidirect product | D127⋊(C3×C25) |
| unambiguous semidirect product | (C127⋊C3)⋊(C2×C25) |
| unambiguous semidirect product | (C25×D127)⋊C3 |
| Fitting, Hall | C25×C127 ⋊ C2×C3 |
| derived, Sylow | C127 ⋊ C2×C3×C25 |
| Hall | C25×C127⋊C3 ⋊ C2 |
| Hall | C25×D127 ⋊ C3 |
| Hall | C127⋊C3 ⋊ C2×C25 |
| Hall | D127 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D127⋊C3 |
| commutator, hypocenter | C127 | C2×C3×C25 |
| Frattini | C5 | C5×D127⋊C3 |
| Fitting | C25×C127 | C2×C3 |
| socle, cosocle | C5×C127 | C2×C3×C5 |
| prime radical | C5×D127⋊C3 | C5 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3175 |
675 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D127⋊C3, C2×C25×D127⋊C3 |
| maximal normal subgroup of | D25×D127⋊C3, C2×C25×D127⋊C3 |
| maximal quotient of | C25×(C127⋊C3)⋊C4, C2×C25×D127⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19050, 10);