Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#13089659⋊C3 |
| unambiguous semidirect product | (C5×#13089659)⋊C3 |
| Fitting, socle, Hall | C5×C192 ⋊ C3×C4 |
| derived, Sylow | C192 ⋊ C3×C4×C5 |
| Hall | C5×#13089659 ⋊ C3 |
| Hall | C5×#11762245 ⋊ C4 |
| Hall | #13089659 ⋊ C3×C5 |
| Hall | #11762245 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #13089659⋊C3 |
| commutator, hypocenter | C192 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C3×C4 |
| prime radical | C5×#14524206 | C2 |
| cosocle | C19⋊D19 | C2×C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 104);