Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C7⋊SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C4×C7⋊SL(2,𝔽3) |
| unambiguous semidirect product | (C2×C4×C7)⋊SL(2,𝔽3) |
| unambiguous semidirect product | (C2×C4×Q8)⋊ΓL(1,𝔽8) |
| Fitting, Hall | C2×C4×C7×Q8 ⋊ C3 |
| derived | C7×Q8 ⋊ C2×C3×C4 |
| Sylow | C2×C4×Q8 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×C4×SL(2,𝔽3) |
216 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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, 10061);