Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)×Dic71 |
| unambiguous semidirect product | C71⋊(C3×C4×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×Dic71)⋊C32 |
| unambiguous semidirect product | (C3×C7×Dic71)⋊C3 |
| derived, Hall | C7×C71 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8)×C71 ⋊ C4 |
| Hall | C7×Dic71 ⋊ C32 |
| Sylow | C71 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C32×Dic71 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5964 |
1110 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 54);