Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#23751432 |
| Fitting, socle, Hall | C2×C132×C19 ⋊ C3 |
| derived, Hall | C132×C19 ⋊ C2×C3 |
| Hall | C2×C132 ⋊ C19⋊C3 |
| Sylow | C132 ⋊ C2×C19⋊C3 |
| Hall | C2×C19 ⋊ #92788 |
| Sylow | C19 ⋊ C2×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #23751432 |
| commutator, cosocle, hypocenter | C132×C19 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C19 | C3 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6422 |
2146 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50310209, #50310211, #50310219, … |
| maximal normal subgroup of | #50310209, #50310211, #50310219, … |
| maximal quotient of | C4×#23751432, C22×#23751432 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 87);