Finite Group DatabasebetaFinite Group Databasebeta| order | 19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C127⋊#3874 |
| Fitting, socle, Hall | C52×C127 ⋊ D3 |
| derived, Hall | C52⋊C3×C127 ⋊ C2 |
| Sylow | C127 ⋊ #3874 |
| Hall | C52⋊C3 ⋊ D127 |
| Sylow | C52 ⋊ D381 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊C3×C127 | C2 |
| Fitting, socle | C52×C127 | D3 |
| LCS | G ▷ C52⋊C3×C127 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1905 |
Polycyclic presentation:
2,3,127,5^2|b^a=b^2,c^a=c^126,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^2706 conjugacy classes — view the full character table.
| maximal subgroup of | #3874×D127, #3874⋊D127, ((C5⋊D5)⋊C3)⋊D127, … |
| maximal normal subgroup of | #3874×D127, #3874⋊D127, ((C5⋊D5)⋊C3)⋊D127, … |
| maximal quotient of | C127⋊#64470, C2×C127⋊#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19050, 20);