Finite Group DatabasebetaFinite Group Databasebeta| order | 1848 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×(C22⋊D7)⋊C3 |
| unambiguous semidirect product | (C22⋊D7)⋊(C3×C11) |
| unambiguous semidirect product | (C11×C22⋊D7)⋊C3 |
| Fitting | C22×C7×C11 ⋊ C2×C3 |
| Hall | C11×C22⋊D7 ⋊ C3 |
| Hall | C11×ΓL(1,𝔽8) ⋊ D4 |
| Hall | C7×C11 ⋊ C3×D4 |
| Hall | C22⋊D7 ⋊ C3×C11 |
| Hall | ΓL(1,𝔽8) ⋊ D4×C11 |
| Sylow | C7 ⋊ C3×D4×C11 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 308 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18)(14,15,17)(20,22);(13,14)(15,17)(16,18)(19,20)(21,22)209 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1848, 29);