Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20297981⋊C3 |
| Fitting, socle, Sylow | C192 ⋊ C3×Dic5 |
| derived, Hall | C192⋊C5 ⋊ C3×C4 |
| Hall | #20297981 ⋊ C3 |
| Hall | #11762245⋊C5 ⋊ C4 |
| Hall | #11762245 ⋊ Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C192⋊C5 | C3×C4 |
| Fitting, socle | C192 | C3×Dic5 |
| prime radical | #14524206⋊C5 | C2 |
| cosocle | (C19⋊D19)⋊C5 | C2×C3 |
| LCS | G ▷ C192⋊C5 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
Polycyclic presentation:
2,3,2,5,19^2|a^2=c,d^a=d^4,e^a=e^16f^10,f^a=e^18f^3,e^b=e^11,f^b=f^11,e^c=e^18,f^c=f^18,e^d=e^7f^13,f^d=e^10f^1630 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 86);