Finite Group DatabasebetaFinite Group Databasebeta| order | 20406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C179 · Schur multiplier (H2) = C1 |
| direct product | C2×C19⋊C3×C179 |
| unambiguous semidirect product | (C2×C19)⋊(C3×C179) |
| unambiguous semidirect product | (C2×C19×C179)⋊C3 |
| Fitting, socle, Hall | C2×C19×C179 ⋊ C3 |
| derived, Sylow | C19 ⋊ C2×C3×C179 |
| Hall | C19×C179 ⋊ C2×C3 |
| Hall | C2×C19 ⋊ C3×C179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C179 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C179 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C179 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C179 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6802 |
3222 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20406, 2);