Finite Group DatabasebetaFinite Group Databasebeta| order | 18411 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17×C19 · Schur multiplier (H2) = C1 |
| direct product | C17×C19×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C17×C19) |
| unambiguous semidirect product | (C17×C19)⋊(C3×C19) |
| Fitting, socle, Hall | C17×C192 ⋊ C3 |
| derived | C19 ⋊ C3×C17×C19 |
| Sylow | C192 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C19 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C17×C19 |
| Frattini | C1 | G |
| Fitting, socle | C17×C192 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C17×C19 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 969 |
2907 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×C19×D19⋊C3, C17×(C19⋊C3)⋊D19, C17×D19×C19⋊C3, … |
| maximal normal subgroup of | C17×C19×D19⋊C3, C17×(C19⋊C3)⋊D19, C17×D19×C19⋊C3, … |
| maximal quotient of | C2×C17×C19×C19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18411, 5);