Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C2 |
| direct product | A4×C211⋊C7 |
| unambiguous semidirect product | C22⋊(C3×C211⋊C7) |
| unambiguous semidirect product | (A4×C211)⋊C7 |
| Fitting, socle, derived, Hall | C22×C211 ⋊ C3×C7 |
| Hall | C22×C211⋊C7 ⋊ C3 |
| Hall | A4×C211 ⋊ C7 |
| Sylow | C211 ⋊ C7×A4 |
| Sylow | C22 ⋊ C3×C211⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C211 | C3×C7 |
| LCS | G ▷ C22×C211 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 844 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 36);