Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C22×(C211⋊C3)⋊C7 |
| unambiguous semidirect product | (C22×C211⋊C3)⋊C7 |
| Fitting, socle, Hall | C22×C211 ⋊ C3×C7 |
| derived, Sylow | C211 ⋊ C22×C3×C7 |
| Hall | C22×C211⋊C7 ⋊ C3 |
| Hall | C22×C211⋊C3 ⋊ C7 |
| Hall | C211⋊C7 ⋊ C22×C3 |
| Hall | C211⋊C3 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | (C211⋊C3)⋊C7 |
| commutator, cosocle, hypocenter | C211 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C211 | C3×C7 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C22 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 844 |
124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 34);