Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#14524209⋊C2 |
| unambiguous semidirect product | #14524209⋊(C2×C5) |
| Fitting, socle, Hall | C5×C192 ⋊ C22×C3 |
| derived, Sylow | C192 ⋊ C22×C3×C5 |
| Hall | C5×D192 ⋊ C3 |
| Hall | C5×#11762246 ⋊ C22 |
| Hall | D192 ⋊ C3×C5 |
| Hall | #11762246 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14524209⋊C2 |
| commutator, cosocle, hypocenter | C192 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C22×C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 570 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 107);