Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C4×C13×SL(2,𝔽3) |
| unambiguous semidirect product | (C4×Q8)⋊(C3×C13) |
| Fitting, Hall | C4×Q8×C13 ⋊ C3 |
| derived | Q8 ⋊ C3×C4×C13 |
| Sylow | C4×Q8 ⋊ C3×C13 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 856);