Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#13093360 |
| Fitting, socle, Hall | C132×C19 ⋊ C2×C3 |
| derived | C13×C19 ⋊ C2×C3×C13 |
| Hall | C13×#10625202 ⋊ C2 |
| Hall | C132×D19 ⋊ C3 |
| Sylow | C132 ⋊ D19⋊C3 |
| Hall | D19 ⋊ C13×C13⋊C3 |
| Sylow | C19 ⋊ C2×C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #13093360 |
| commutator, cosocle, hypocenter | C13×C19 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C132×C19 | C2×C3 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 741 |
689 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#13093360⋊C2, #13093360⋊D13, D13×#13093360, … |
| maximal normal subgroup of | C13×#13093360⋊C2, #13093360⋊D13, D13×#13093360, … |
| maximal quotient of | C13×#15688279, C2×C13×#13093360 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 33);