Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×ΓL(1,𝔽8)⋊C4 |
| derived, Sylow | C7 ⋊ C22×C3×C42 |
| Hall | C22×C4×Dic7 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C22×C42 |
996 conjugacy classes of subgroups; only the 616 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 616 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C42×AGL(1,𝔽7), C22×#6503⋊C3 |
| maximal normal subgroup of | C22×C42×AGL(1,𝔽7), C22×#6503⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6805);