Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic71⋊C7) |
| unambiguous semidirect product | (C71⋊C7)⋊Dic9 |
| unambiguous semidirect product | Dic639⋊C7 |
| derived, Hall | C9×C71 ⋊ C4×C7 |
| Hall | C9×C71⋊C7 ⋊ C4 |
| Hall | Dic639 ⋊ C7 |
| Hall | C71⋊C7 ⋊ Dic9 |
| Sylow | C71 ⋊ C7×Dic9 |
| Sylow | C9 ⋊ Dic71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊(D71⋊C7) |
| commutator, hypocenter | C9×C71 | C4×C7 |
| Frattini | C2×C3 | C3⋊(D71⋊C7) |
| Fitting, cosocle | C2×C9×C71 | C2×C7 |
| socle | C2×C3×C71 | D3×C7 |
| prime radical | C2×C3×C71⋊C7 | D3 |
| LCS | G ▷ C9×C71 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2556 |
Polycyclic presentation:
2,3,7,71,2,3|a^2=e,b^3=f^2,b^a=b^2f,d^a=d^70,f^a=f^2,d^c=d^45174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 13);