Finite Group DatabasebetaFinite Group Databasebeta| order | 19053 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#10620323 |
| Fitting, socle, Hall | C29×C73 ⋊ C9 |
| derived, Sylow | C73 ⋊ C9×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #10620323 |
| commutator, hypocenter | C73 | C9×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C73 | C9 |
| prime radical | C29×C73⋊C3 | C3 |
| cosocle | C73⋊C3 | C3×C29 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2117 |
493 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C29×#10620323⋊C2, C29⋊(#10620323⋊C2), D29×#10620323, … |
| maximal normal subgroup of | C29×#10620323⋊C2, C29⋊(#10620323⋊C2), D29×#10620323, … |
| maximal quotient of | C2×C29×#10620323 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19053, 4);