Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D7⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | Dic7⋊(C42⋊C3) |
| derived | C42×C7 ⋊ C3×C4 |
| Hall | C42×Dic7 ⋊ C3 |
| Sylow | C7 ⋊ C4×C42⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7⋊(C42⋊C3) |
| commutator, hypocenter | C42×C7 | C3×C4 |
| Frattini | C23 | D7⋊A4 |
| Fitting, cosocle | C2×C42×C7 | C2×C3 |
| socle | C23×C7 | C2×A4 |
| prime radical | C2×C7⋊(C42⋊C3) | C2 |
| LCS | G ▷ C42×C7 | |
| UCS | C1 ◁ C2 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
Polycyclic presentation:
2,3,2^3,7,2^2|a^2=c,d^2=g,e^2=gh,f^a=f^6,d^b=de,e^b=dgh,f^b=f^2,g^b=h,h^b=gh64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1462);