Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×C22⋊#11762245 |
| unambiguous semidirect product | C22⋊(C5×#11762245) |
| unambiguous semidirect product | (C22×C5)⋊#11762245 |
| Fitting, socle, Hall | C22×C5×C192 ⋊ C3 |
| derived, Hall | C22×C192 ⋊ C3×C5 |
| Hall | C5×C192 ⋊ A4 |
| Sylow | C192 ⋊ C5×A4 |
| Hall | C22×C5 ⋊ #11762245 |
| Sylow | C22 ⋊ C5×#11762245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C22⋊#11762245 |
| commutator, cosocle, hypocenter | C22×C192 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C192 | C3 |
| LCS | G ▷ C22×C192 | |
| UCS | C1 ◁ C5 | |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7220 |
2420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 202);