Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | D4×C4⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (D4×D28)⋊C3 |
| Fitting | C4×C7×D4 ⋊ C2×C3 |
| Hall | D4×D28 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ D42 |
| Sylow | C7 ⋊ C3×D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×AGL(1,𝔽7) |
| commutator, socle, cosocle | C22×C7 | C24×C3 |
| Fitting | C4×C7×D4 | C2×C3 |
| hypercenter | C4×D4 | AGL(1,𝔽7) |
| hypocenter | C7 | C3×D42 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | #72229268, #72229295, #72229420, … |
| maximal normal subgroup of | #72229268, #72229295, #72229420, … |
| maximal quotient of | #72229599, #72229611, #72259691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6575);