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 | C4×#41⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C4×#41)⋊ΓL(1,𝔽8) |
| Fitting, Hall | C4×C7×#41 ⋊ C3 |
| Sylow | C4×#41 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C4×#41⋊C3 |
180 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 54 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, 10062);