Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C19 |
| direct product | C3×#13089659⋊C5 |
| unambiguous semidirect product | (C3×#13089659)⋊C5 |
| Fitting, socle, Hall | C3×C192 ⋊ C4×C5 |
| derived, Sylow | C192 ⋊ C3×C4×C5 |
| Hall | C3×C192⋊C5 ⋊ C4 |
| Hall | C3×#13089659 ⋊ C5 |
| Hall | C192⋊C5 ⋊ C3×C4 |
| Hall | #13089659 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13089659⋊C5 |
| commutator, hypocenter | C192 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C192 | C4×C5 |
| prime radical | C3×(C19⋊D19)⋊C5 | C2 |
| cosocle | C19⋊D19 | C2×C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 570 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 92);