Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C7⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C22×C7⋊(C42⋊C3) |
| Fitting, Hall | C22×C42×C7 ⋊ C3 |
| derived | C42×C7 ⋊ C22×C3 |
| Sylow | C22×C42 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C22×C42⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C7⋊(C42⋊C3) |
| commutator, cosocle, hypocenter | C42×C7 | C22×C3 |
| Frattini | C22 | C22×C22⋊ΓL(1,𝔽8) |
| Fitting | C22×C42×C7 | C3 |
| socle | C24×C7 | A4 |
| LCS | G ▷ C42×C7 | |
| UCS | C1 ◁ C22 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10057);