Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(#11762245⋊C5) |
| unambiguous semidirect product | (C192⋊C5)⋊A4 |
| unambiguous semidirect product | (C22⋊#11762245)⋊C5 |
| Fitting, socle, derived, Hall | C22×C192 ⋊ C3×C5 |
| Hall | C22×C192⋊C5 ⋊ C3 |
| Hall | C22⋊#11762245 ⋊ C5 |
| Hall | C192⋊C5 ⋊ A4 |
| Sylow | C192 ⋊ C5×A4 |
| Sylow | C22 ⋊ #11762245⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C192 | C3×C5 |
| LCS | G ▷ C22×C192 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 380 |
Polycyclic presentation:
3,5,2^2,19^2|c^a=cd,d^a=c,e^a=e^11,f^a=f^11,e^b=e^12f^8,f^b=e^14f^11116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 100);