Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C2×C19×#92788 |
| Fitting, socle, Hall | C2×C132×C19 ⋊ C3 |
| derived, Sylow | C132 ⋊ C2×C3×C19 |
| Hall | C132×C19 ⋊ C2×C3 |
| Hall | C2×C132 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | #92788 |
| commutator, cosocle, hypocenter | C132 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C19 | C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C19 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6422 |
2242 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#14523128, #50310213, C19×#14523130, … |
| maximal normal subgroup of | C19×#14523128, #50310213, C19×#14523130, … |
| maximal quotient of | C4×C19×#92788, C22×C19×#92788 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 88);