Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#16813380⋊C2)⋊C3 |
| unambiguous semidirect product | (#16813380⋊C3)⋊C2 |
| unambiguous semidirect product | (#14524206⋊C5)⋊C2 |
| Fitting, socle, Sylow | C192 ⋊ C2×C3×D5 |
| derived, Hall | C192⋊C5 ⋊ C22×C3 |
| Hall | #16813380⋊C2 ⋊ C3 |
| Hall | #11762245⋊C5 ⋊ C22 |
| Hall | #11762245 ⋊ C2×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C192⋊C5 | C22×C3 |
| Fitting, socle | C192 | C2×C3×D5 |
| LCS | G ▷ C192⋊C5 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 95 |
Polycyclic presentation:
2^2,3,5,19^2|e^a=e^18,f^a=f^18,d^b=d^4,e^b=e^2f^4,f^b=e^4f^17,e^c=e^11,f^c=f^11,e^d=e^16f^4,f^d=e^6f^1739 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 85);