Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#66659 |
| Fitting | C4×C7×Q8 ⋊ C2×C3 |
| Hall | C4×#1161 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C4×#41 |
| Sylow | C7 ⋊ C3×C4×#41 |
620 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 282 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#66659, C4×#6477⋊C3, #72218565, … |
| maximal normal subgroup of | C4×#6477⋊C3, #72218565, C4×#41×AGL(1,𝔽7), … |
| maximal quotient of | AGL(1,𝔽5)×#66659 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6596);