Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic211⋊C7) |
| unambiguous semidirect product | (C211⋊C7)⋊Dic3 |
| unambiguous semidirect product | Dic633⋊C7 |
| derived, Hall | C3×C211 ⋊ C4×C7 |
| Hall | C3×C211⋊C7 ⋊ C4 |
| Hall | Dic633 ⋊ C7 |
| Hall | C211⋊C7 ⋊ Dic3 |
| Sylow | C211 ⋊ C7×Dic3 |
| Sylow | C3 ⋊ Dic211⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D211⋊C7) |
| commutator, hypocenter | C3×C211 | C4×C7 |
| Fitting, socle, cosocle | C2×C3×C211 | C2×C7 |
| prime radical | C2×C3×C211⋊C7 | C2 |
| LCS | G ▷ C3×C211 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2532 |
Polycyclic presentation:
2,3,7,211,2|a^2=e,b^a=b^2,d^a=d^210,d^c=d^171132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 17);