Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#16813380⋊C2 |
| Fitting, socle, Hall | C3×C192 ⋊ C2×D5 |
| derived, Hall | C192⋊C5 ⋊ C22×C3 |
| Hall | C3×C192⋊C5 ⋊ C22 |
| Sylow | C192 ⋊ C2×C3×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16813380⋊C2 |
| commutator, cosocle, hypocenter | C192⋊C5 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C192 | C2×D5 |
| LCS | G ▷ C192⋊C5 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 285 |
159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 90);