Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | Dic9×C71⋊C7 |
| unambiguous semidirect product | C9⋊(C4×C71⋊C7) |
| unambiguous semidirect product | (Dic9×C71)⋊C7 |
| derived, Hall | C9×C71 ⋊ C4×C7 |
| Hall | C9×C71⋊C7 ⋊ C4 |
| Hall | Dic9×C71 ⋊ C7 |
| Sylow | C71 ⋊ C7×Dic9 |
| Sylow | C9 ⋊ C4×C71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C71⋊C7 |
| commutator, hypocenter | C9×C71 | C4×C7 |
| Frattini | C2×C3 | D3×C71⋊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 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 12);