Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C7⋊SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C8×C7⋊SL(2,𝔽3) |
| unambiguous semidirect product | (C7×C8)⋊SL(2,𝔽3) |
| unambiguous semidirect product | (C8×Q8)⋊ΓL(1,𝔽8) |
| Fitting, Hall | C7×C8×Q8 ⋊ C3 |
| derived | C7×Q8 ⋊ C3×C8 |
| Sylow | C8×Q8 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C8×SL(2,𝔽3) |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4363);