Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C71 · Schur multiplier (H2) = C1 |
| direct product | C4×C7⋊C9×C71 |
| unambiguous semidirect product | (C4×C7)⋊(C9×C71) |
| unambiguous semidirect product | (C4×C7×C71)⋊C9 |
| derived, Sylow | C7 ⋊ C4×C9×C71 |
| Hall | C4×C7×C71 ⋊ C9 |
| Hall | C7×C71 ⋊ C4×C9 |
| Hall | C4×C7 ⋊ C9×C71 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17892 |
4260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 3);