Finite Group DatabasebetaFinite Group Databasebeta| order | 19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×D127 |
| Fitting, socle, Hall | C3×C52×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C2×C3×C52 |
| Hall | C52×C127 ⋊ C2×C3 |
| Hall | C3×C127 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | D127 |
| commutator, cosocle, hypocenter | C127 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C127 | C2 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C3×C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9525 |
4875 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D5×D127, C3×C5⋊D5×D127, C52×D3×D127, … |
| maximal normal subgroup of | C3×C5×D5×D127, C3×C5⋊D5×D127, C52×D3×D127, … |
| maximal quotient of | C3×C52×Dic127, C2×C3×C52×D127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19050, 40);