Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#1159⋊C3 |
| unambiguous semidirect product | (C4×#1159)⋊C3 |
| Fitting | C4×C7×D4 ⋊ C2×C3 |
| Hall | C4×#1159 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C4×#41 |
| Sylow | C7 ⋊ C3×C4×#41 |
620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1159⋊C3, C4×#6474⋊C3, #72218539, … |
| maximal normal subgroup of | C4×#6474⋊C3, #72218539, C4×#41×AGL(1,𝔽7), … |
| maximal quotient of | AGL(1,𝔽5)×#1159⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6571);