Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#23751423 |
| Fitting, Hall | C2×C19×C169 ⋊ C3 |
| derived, Hall | C19×C169 ⋊ C2×C3 |
| Hall | C2×C169 ⋊ C19⋊C3 |
| Sylow | C169 ⋊ C2×C19⋊C3 |
| Hall | C2×C19 ⋊ C169⋊C3 |
| Sylow | C19 ⋊ C2×C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #23751423 |
| commutator, cosocle, hypocenter | C19×C169 | C2×C3 |
| Frattini | C13 | C2×#10625202 |
| Fitting | C2×C19×C169 | C3 |
| socle | C2×C13×C19 | C13⋊C3 |
| LCS | G ▷ C19×C169 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6422 |
2146 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50310124, #50310128, #50310130, … |
| maximal normal subgroup of | #50310124, #50310128, #50310130, … |
| maximal quotient of | C4×#23751423, C22×#23751423 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 16);