Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C211 · Schur multiplier (H2) = C1 |
| direct product | C4×ΓL(1,𝔽8)×C211 |
| unambiguous semidirect product | (C4×C7)⋊(C3×C211) |
| Fitting, Hall | C4×C7×C211 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C4×C211 |
| Hall | C7×C211 ⋊ C3×C4 |
| Hall | C4×C7 ⋊ C3×C211 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5908 |
4220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 4);